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Quadratic equation with complex roots

Which equations define

y

as a linear function of

x

? Select all that apply.

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Multi-select Choices:

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y = \sqrt[3]{27}

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y = 5x + 9

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4y = 4x^2 - 8

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y = \frac{2}{5} + x

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x - y = 10

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y = 8x - 2x + 4

Which equations define

y

as a linear function of

x

? Select all that apply.

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Multi-select Choices:

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y = 5x^3

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y - 4 = x^5

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-3y = 12

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y = \frac{4x^2}{5}

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y = -2 + 12x

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3x - y = 9

Select all of the equations below that are equivalent to:

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p + q = 33

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Use properties of equality.

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Multi-select Choices:

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(p + q) \cdot -3 = -99

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(p + q) \cdot 2 = 66

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3(p + q) = 99

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(p + q) \cdot -2 = -66

4

. Solve the following system of equations. (Hint: Use the quadratic formula.)

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\begin{array}{l} f(x)=2 x^{2}-3 x-10 \\ g(x)=-3 x^{2}+20 \end{array}

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(-2.2,5.9)

(3.2,0.9)

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(0,-10)

(1,17)

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(2.8,-3.0)

(-1.5,-1)

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(-2.2,5.9)

(2.8,-3.0)

4

. Solve the following system of equations. (Hint: Use the quadratic formula.)

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f(x)=2 x^{2}-3 x-10

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=-3 x^{2}+20

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(-2.2,5.9)

(3.2,0.9)

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(0,-10)

(1,17)

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(2.8,-3.0)

(-1.5,-1)

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(-2.2,5.9)

(2.8,-3.0)

3

. Which of the following accurately shows the first step when solving the following system of equations by substitution?

f(x)=-5 x^{2}+2 x+7

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g(x)=-3 x+4

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-5 x^{2}+2 x+7-63 x+4=0

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g(x)=-3\left(-5 x^{2}+2 x+7\right)+4

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-5 x^{2}+2 x+7=-3 x+4

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f(x)=-5(-3 x+4)^{2}+2(-3 x+4)+7

Solve the quadratic equation

x^{2}-x-6=0

Solve the equation for all values of

\mathrm{x}

in simplest form:

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(x-9)^{2}=-1

5

\frac{2^{x-1}+2^{x}}{2^{x+1}-2^{x}}=\frac{3}{2}

Is this function linear, quadratic, or exponential?

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

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x

y

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-3

0

1

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-2

0

3

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-1

0

9

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0

2

7

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1

8

1

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A table of values for the quadratic function

f

is shown below. If

3

is one solution, what is the value of the other solution?

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\begin{tabular}{|c|l|}

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x

f(x)

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-8

-2

75

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-7

0

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-6

2

25

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-5

4

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-4

5

25

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-3

6

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-2

6

25

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-1

6

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0

5

25

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1

4

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Find the quadratic function that is the best fit for

f(x)

defined by the table below.

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

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\mathbf{x}

0

2

4

6

8

10

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\mathbf{f ( x )}

0

397

1603

3605

6402

9999

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The quadratic function is

y=\square x^{2}+\square x+(\square)

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(Type an integer or decimal rounded to two decimal places as needed.)

Rearrange the formula

\quad p=\frac{3 h^{2}}{5}

h

\sqrt[3]{5 x-2}=\frac{1}{5}\left(x^{3}+2\right)

Find real zeros of

p(x)=x^3-4x^2+6x-24

f(x)=x^{2}-6x-7

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Which of the following is an equivalent form of the function

f

in which the zeros of

f

appear as constants or coefficients?

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1

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f(x)=(x-7)(x+1)

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f(x)=(x-1)(x+7)

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f(x)=x(x-6)-7

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f(x)=(x-6)^{2}-7

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Solve the equation for all real solutions in simplest form.

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t^{2}+3 t-19=-5

y=x^{2}+6 x+2

Quadratic Formu.

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1

. Solve the following equa

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2 x^{2}+x-3=0

How to factor using quadratic formula

3x^2+4x-6

Practice problems

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Find the zeros of the Folynomial functions

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f(x)=x^{3}+8 x^{2}+11 x-20

Use the quadratic formula to solve. Express your answer in simplest form.

5r^2 +24r-3= 2

11

) Use the Quadratic Formula to determine the solution(s) to

0=2 x^{2}-3 x-5

Use the Quadratic Formula to solve the quadratic below:

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x^{2}-5x+9=0

Use the Quadratic Formula to solve the quadratic below

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x^{2}-5 x+9=0

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Desmos Scientific Calculator

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Solve using the quadra

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x^{2}=2 x+1

Which equation represents a linear function?

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y=-x^{2}-4

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-3 x^{2}+1=y

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y=x^{2}

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x+2=y

y=\sqrt[3]{x^{2}+x+1}

Find the equation of the tangent line to

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x=\sqrt[3]{t}

y=\frac{1}{2}(t^{2}-2)

(2,31)

Which of the following is equivalent to the expression

3 x^{2}+21 x+18

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1

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3(x+1)(x+6)

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3(x+2)(x+3)

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3(x+2)(x+9)

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3(x+3)(x+4)

Which equation shows the commutative property of multiplication?

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f \cdot (g \cdot h) = (f \cdot g) \cdot h

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f \cdot 0 = 0

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f \cdot g = g \cdot f

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h = f \cdot g

(t+1)^{2}+c=0

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In the given equation,

c

is a constant. The equation has solutions at

t=\frac{3}{2}

t=-\frac{7}{2}

. What is the value of

c

Set up the quadratic formula that you would use to solve:

x^{2}-3 x-1=0

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x=\frac{m \pm \sqrt{p}}{q}

(fill in the value of the indicated variables)

3

. Solve the rational equation:

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\frac{x}{x+3}=\frac{8}{x+6}

1

. Find all Roots of

P(x)=x^{4}-6 x^{3}-11 x^{2}+12 x-26

3+2 i

(a x+5)(x+v)=a x^{2}+25 x+25

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What is the value of

a

in the given equation?

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1

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-5

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-4

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4

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5

Select all of the equations below that are equivalent to:

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9 = n + -3

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Use properties of equality.

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Multi-select Choices:

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64 = (n + -3) \cdot 8

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-77 = -7(n + -3)

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90 = (n + -3) \cdot 10

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63 = (n + -3) \cdot 7

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3 / 26 / 24

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8

5

SOLVING QUADRATICS BY COMPLETING THE SQUARE

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1

. Which trinomial is equivalent to

(x-8)^{2}

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1

x^{2}-8 x-16

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2

x^{2}-8 x+16

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3

x^{2}-16 x+64

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4

x^{2}-16 x-64

5

. Determine the exact intersection point of lines

3 y=6 x-5

3 x=7 y-\frac{109}{3}

2

8

-112

d. Factor and use the Zero Product Property to find the solutions of the quadratic equation:

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0=x^{2}+12 x+36

Re-write the quadratic function below in Standard Form:

y= -6(x-1)(x-5)

\lim_{x \to 10}\frac{x^{2}-100}{x-9}

Use the quadratic formula to solve. Express your answer in simplest form.

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3c^{2}+14c-8=4c

A quadratic equation is in the form

ax^2+bx+c=0

. If the roots of the quadratic equation

2x^2-4x+k=0

are real and equal, find the value of

k

Solve the equation for all real solutions in simplest form.

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2a^{2}-5a-2=-3a^{2}

3х + 2y = 4(x-y-6)

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6(у + x)=7x-24

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Which of the following accurately describes all solutions to the system of equations shown?

Find the zeros of the following quadratic function using the square root method. What are the

x

-intercepts of the graph of the function?

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F(x)=(2 x+9)^{2}-32

Find the zeros of the quadratic function using the square root method. What are the

x

-intercepts of the graph of the function?

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g(x)=(x-3)^{2}-1

Find the zeros of the following quadratic function using the square root method. What are the x-intercepts of the graph of the function?

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f(x)=x^{2}-50

Write the quadratic equation in standard form:

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x+3=-3 x^{2}

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