Resources

Resources

Write a quadratic function from its x-intercepts and another point

Select the expressions that are equivalent to

7(n + 1)

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Multi-select Choices:

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7n + 7

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8n

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1(7 + n)

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(1 + n)7

Identify the center and radius.

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3

x^{2}+(y+2)^{2}=64

Identify the center and radius.

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2

(x-2)^{2}+(y+3)^{2}=36

14

. The parametric equation of the line with equations

x=-1+2 t

y=7+3 t

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\frac{3}{2}

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0

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\frac{2}{3}

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Write the equation of the parabola that passes through the points

(-5,-36)

(-3,0)

(-2,0)

. Write your answer in the form

y=a(x–p)(x–q)

a

p

q

are integers, decimals, or simplified fractions.

Write an equation for the quadratic function

f

whose graph passes through the points

(6,0),(7,0)

(5,6)

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f(x)=

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1

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What is the value of the expression

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2x^{3}y

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x=-2

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y=3

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1

-192

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2

-108

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3

-48

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4

48

Write a quadratic equation for a parabola that passes through the points

(-1,-3)

(0,-4)

(2,6)

using quadratic regression.

16

. Write a quadratic function in standard form that passes through

(-2,0),(4,0)

(2,-8)

2

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i) Solve the quadratic Equation

-x^{2}+x-2=0

-2014

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r

r(\cos \theta+i \sin \theta)

Statistics - Question

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Solve the following problem and choose the best answer.

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Which of the following points

(x, y)

lies on the graph of

8 x+2 y=24 ?

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(-1,8)

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(2,8)

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(6,-12)

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(8,2)

Function A is a linear function whose graph includes the points

(-8,-21)

(8,-7)

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Which of the following functions has the same slope as Function A?

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y = \frac{7}{8}x + 14

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y = -14x + \frac{7}{8}

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y = 14x - \frac{7}{8}

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y = -\frac{7}{8}x - 14

Function A is a linear function whose graph includes the points

(0,-7)

(3,0)

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Which of the following functions has the same

y

-intercept as Function A?

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y = -7

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y = \frac{7}{3}x

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y = -\frac{7}{3}x

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y = 3

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\begin{array}{r} 2 \frac{1}{2}+x=3 \frac{1}{4} \quad \begin{array}{r} 3 \frac{1}{4} \frac{2}{8} \\ 2 \frac{1}{2} \frac{4}{8} \end{array} \\ 2 \frac{1}{2}+1 \frac{3}{4} \frac{2}{8 y} \end{array}

Algebra I Regents Exam Questions by State Standar www.jmap.org

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438

Which expression is equivalent to

36 x^{2}-100

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1

4(3 x-5)(3 x-5)

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2

4(3 x+5)(3 x-5)

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3

2(9 x-25)(9 x-25)

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4

2(9 x+25)(9 x-25)

Write the equation in standard form

f(x) = ax^2 + bx + c

(0, -12)

(1, -9)

(-2, -36)

Write the equation of the quadratic function given the three points on the function. Write the equation in standard form

f(x) = ax^2 + bx + c

(0, -12)

(1, -9)

(-2, -36)

Write the equation of the quadratic function given the three points on the function. Write the equation in standard form

f (x) = ax^2 +bx+ c

(0, -5)

(2, 27)

(-2, -5)

A quadratic equation is graphed. Which of the following linear equations combines with the graphed equation to create a system of equations whose solutions are the points

\left(3, \frac{5}{2}\right)

(-2,-5)

1342

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Final Exam, Fall

2023

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Find a standard equation for the plane containing the line

\vec{L}(t)=(-4,0,6)+t(3,5,1)

(2,1,3)

The table represents some points on the graph of a linear function.

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\begin{tabular}{|r|c|}

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x

y

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-20

-268

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-14

-196

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-8

-124

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-1

-40

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Which equation represents the same relationship?

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y+268=\frac{1}{12}(x+20)

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y+20=\frac{1}{12}(x+268)

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y+268=12(x+20)

18p-36

to identify the equivalent expressions.

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2

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3(9p-12)

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9(2p-4p)

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2(9p-18)

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18(p-2)

99-45 f+36 b

to identify the equivalent expressions.

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2

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9(11-5f+4b)

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3(33-15+12)

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11(9-4f+3b)

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3(33-15 f+12 b)

x=-b \pm \sqrt{b^{2}}

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1

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Solve each equation with th

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1

2 n^{2}=-9 n+126

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-2 n

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-2 n^{2}

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-2 n^{2}-9 n+126=

p

x=-2, x=\frac{1}{3}

x=3

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What could be the equation of

p

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1

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p(x)=(x+2)(x+3)(3 x+1)

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p(x)=(x+2)(x+3)(3 x-1)

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p(x)=(x+2)(x-3)(3 x-1)

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p(x)=(x-2)(x+3)(3 x+1)

p

x=0, x=-\frac{1}{6}

x=-3

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What could be the equation of

p

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1

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p(x)=x(6 x+1)(x+3)

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p(x)=x(6 x-1)(x-3)

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p(x)=x\left(\frac{1}{6} x\right)(x+3)

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p(x)=x\left(-\frac{1}{6} x\right)(x-3)

p

x=5, x=-1

x=-\frac{1}{4}

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What could be the equation of

p

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1

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p(x)=(x+5)(x+1)(4 x+1)

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p(x)=(x-5)(x+1)(4 x+1)

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p(x)=(x+5)(x-1)(4 x-1)

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p(x)=(5 x)(-1 x)\left(-\frac{1}{4} x\right)

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Write the given sum as a single column matrix

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1

3 t\left(\begin{array}{c}2 \\ t \\ -1\end{array}\right)+(t-1)\left(\begin{array}{c}-1 \\ -t \\ 3\end{array}\right)-2\left(\begin{array}{c}3 t \\ 4 \\ -5 t\end{array}\right)

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2

\left(\begin{array}{ccc}1 & -3 & 4 \\ 2 & 5 & -1 \\ 0 & -4 & -2\end{array}\right)\left(\begin{array}{c}t \\ 2 t-1 \\ -t\end{array}\right)+\left(\begin{array}{c}-t \\ 1 \\ 4\end{array}\right)-\left(\begin{array}{c}2 \\ 8 \\ -6\end{array}\right)

13

A

(-6,7), B

(-2,7)

C

(1,1)

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(a) Quadrilateral

A B C D

has rotational symmetry about the midpoint of

A C

. Find the coordinates of

D

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(b) Find the equation of

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A B

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A D

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(c) Find the coordinates of the point where

A D

(-6,7), B

1

Isosceles triangle JKL has a perimeter of

32

units and the given vertices.

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(-3,-9)

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K(-3,6)

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(x,-1.5)

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What is a possible

x

-coordinate for point

L

A cubic function is graphed in the

x y

-plane. Which of the foll equations could represent the graph?

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1

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y=x(x-1)(x+2)

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y=x(x+1)(x-2)

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y=-x(x-1)(x+2)

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y=-x(x+1)(x-2)

A circle is graphed. Which of the following represents all solutions

(x, y)

to the system of equations created by the equation of this graph and the linear equation

x-y=3

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1

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(-3,0)

(-5,-3)

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(3,0)

(5,-3)

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(-3,0)

(4,-7)

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(3,0)

(-4,-7)

\frac{a}{x+a}+\frac{b}{x-b}=\frac{a+b}{x+c}

x

Advanced Questions

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9

Find, without differentiation, the equation of the straight lines which pass through the point

(4,0)

and are tangential to the circle

(x+1)^{2}+y^{2}=4

2

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4

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\begin{array}{l} \text { Halle: } \quad \text { Y }-7.4-4 B-12 \\ S=A-5\{7-4[6-(7-18+6-8)+5]\} \\ B=(14-9+3+4+5)(18+(-6)(3)-1)+(5-8)(-4) \end{array}

The equation of a curve is

y=2-x-\frac{2 x+3}{x-3}

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\frac{\mathrm{d} y}{\mathrm{~d} x}

\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}

C

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y=2+10x^{\frac{1}{2}}-2x^{\frac{3}{2}},\quad x > 0

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(a)

\frac{dy}{dx}

giving your answer in simplest form.

1

5

8

. Given the cdf

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F(x)=\left\{\begin{array}{ll} 0 & x<-1 \\ \frac{x+2}{4} & -1 \leq x<1 \\ 1 & 1 \leq x . \end{array}\right.

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Sketch the graph of

F(x)

and then compute:

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P\left(-\frac{1}{2}<X \leq \frac{1}{2}\right)

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P(X=0)

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P(X=1)

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P(2<X \leq 3)

A function is shown:

f(x)=36 x^{2}-1

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Choose the equivalent function that best shows the

x

-intercepts on the graph. (

1

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f(x)=18\left(x^{2}-1\right)

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f(x)=(18 x+1)(18 x-1)

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f(x)=6\left(x^{2}+1\right)

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f(x)=(6 x+1)(6 x-1)

x y

-plane, the graph of a rational function

f

has a vertical asymptote at

x=-5

. Which of the following could be an expression for

f(x)

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\frac{(x-5)(x+5)}{2(x-5)}

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\frac{(x-4)(x+5)}{(x-1)(x+5)}

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\frac{(x+1)(x+5)}{(x-5)(x+2)}

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\frac{(x-5)(x-3)}{(x-3)(x+5)}

Given the set of zeros

\{-5,1, \pm 2 i\}

, which is a polynomial of least degree in factored form with a leading coefficient of one?

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f(x)=(x-5)(x+1)\left(x^{2}-4\right)

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f(x)=(x+5)(x-1)\left(x^{2}+2\right)

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f(x)=(x-5)(x+1)(x+2 i)^{2}

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f(x)=(x+5)(x-1)\left(x^{2}+4\right)

Write the equation of the parabola that passes through the points

(1,0)

(3,0)

(5,40)

. Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.

Write the equation of the parabola that passes through the points

(-4,18)

(-3,0)

(-1,0)

. Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.

Write the equation of the parabola that passes through the points

(1,0)

(6,0)

(7,30)

. Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.

Write the equation of the parabola that passes through the points

(-6,-15)

(-1,0)

(-7,0)

. Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.

Write the equation of the parabola that passes through the points

(-3,-14

(-5,0

(2,0

). Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.

Write the equation of the parabola that passes through the points

(3,0)

(2,-27)

(-1,0)

. Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.

Write the equation of the parabola that passes through the points

(-3,0

(-2,-60

(4,0

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Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.

Write the equation of the parabola that passes through the points

(-3,0

(-2,-12

(1,0

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Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.

Write the equation of the parabola that passes through the points

(-9,-16

(-5,0

(-4,0

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Write your answer in the form

y = a(x - p)(x - q)

a

p

q

are integers, decimals, or simplified fractions.