Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the $a$ value of a parabola that has a vertex at $(-3,-4)$ and the point $(-6,-\frac{25}{4})$ that lies on the curve.

View step-by-step help

View step-by-step help

Write equations of parabolas in vertex form using properties

Full solution

Q. Find the

a

value of a parabola that has a vertex at

(-3,-4)

and the point

(-6,-\frac{25}{4})

that lies on the curve.

Identify Vertex Form: Identify the vertex form of a parabola. $\newline$ Vertex form: $y = a(x-h)^2 + k$
Plug in Vertex: Plug in the vertex $(-3,-4)$ into the vertex form. $\newline$ $y = a(x+3)^2 - 4$
Substitute Point for 'a': Substitute the point $(-6,-\frac{25}{4})$ into the equation to find 'a'. $\newline$ $-\frac{25}{4} = a(-6+3)^2 - 4$
Simplify Equation: Simplify the equation. $\newline$ $-\frac{25}{4} = a(-3)^2 - 4$ $\newline$ $-\frac{25}{4} = 9a - 4$
Move Terms: Move $-4$ to the left side of the equation. $\newline$ $-\frac{25}{4} + 4 = 9a$ $\newline$ $-\frac{25}{4} + \frac{16}{4} = 9a$
Combine Fractions: Combine the fractions on the left side. $\newline$ $(-25 + 16)/4 = 9a$ $\newline$ $-9/4 = 9a$
Divide to Solve for 'a': Divide both sides by $9$ to solve for 'a'. $\newline$ $-\frac{9}{4} \div 9 = a$ $\newline$ $-\frac{9}{4} \times \frac{1}{9} = a$
Multiply Fractions: Multiply the fractions to find $a$ . $a = \frac{-9}{36}$ $a = \frac{-1}{4}$

More problems from Write equations of parabolas in vertex form using properties

Question

What is the focus of the parabola

y = -x^2

\newline

Simplify any fractions.

\newline

(_____ , _____)

\newline

Posted 2 months ago

Question

The equation of a parabola is

y = x^2 - 10x + 25

. Write the equation in vertex form.

\newline

Write any numbers as integers or simplified proper or improper fractions.

\newline

Posted 3 months ago

Question

In which direction does the parabola

x + y^2 = -7

\newline

\newline

\text{up}

\newline

\text{down}

\newline

\text{right}

\newline

\text{left}

Posted 3 months ago

Question

What is the vertex of the parabola

y = -4(x - 2)^2 + 2

?

\newline

(\_,\_)

Posted 3 months ago

Question

What is the axis of symmetry of the parabola

x = \frac{1}{2}(y + 3)^2 + 5

Posted 3 months ago

Question

In which direction does the parabola

x - 2y^2 = -5

\newline

\newline

\text{[A]up}

\newline

\text{[B]down}

\newline

\text{[C]right}

\newline

\text{[D]left}

Posted 3 months ago

Question

What is the vertex of the parabola

y - 8x^2 = 4

\newline

(\_,\_)

Posted 2 months ago

Question

The equation of a circle is

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

. What are the center and radius of the circle?

\newline

1

\newline

(A) The center is

(-4,0)

and the radius is

1

\newline

(B) The center is

(4,0)

and the radius is

1

\newline

(C) The center is

(0,4)

and the radius is

1

\newline

(D) The center is

(0,-4)

and the radius is

1

Posted 4 months ago

Question

y=(x-3)(x+9)

\newline

The given equation is graphed in the

x y

-plane. Which of the following are

x

-intercepts of the graph?

\newline

1

\newline

-3

-9

\newline

-3

9

\newline

3

-9

\newline

3

9

Posted 4 months ago

Question

y=2 x^{2}-5 x+7

is graphed in the

x y

-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?

\newline

1

\newline

x

\newline

y

\newline

x

-coordinate of the vertex

\newline

y

-coordinate of the vertex

Posted 4 months ago