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The equation of a parabola is $y = x^2 + 8x + 18$ . Write the equation in vertex form. $\newline$ Write any numbers as integers or simplified proper or improper fractions. $\newline$ ______

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Convert equations of parabolas from general to vertex form

Full solution

Q. The equation of a parabola is

y = x^2 + 8x + 18

. Write the equation in vertex form.

\newline

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

\newline

______

Identify vertex form: Identify the vertex form of a parabola. $\newline$ The vertex form of a parabola is given by the equation $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Complete the square: Complete the square to rewrite the given equation in vertex form. $\newline$ The given equation is $y = x^2 + 8x + 18$ . To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial with the $x$ -terms.
Calculate value: Calculate the value needed to complete the square. $\newline$ We take half of the coefficient of the $x$ -term, which is $8$ , and square it to get $(\frac{8}{2})^2 = 4^2 = 16$ . This is the value we will add and subtract to complete the square.
Rewrite equation: Rewrite the equation by adding and subtracting the value found in Step $3$ . $\newline$ $y = x^2 + 8x + 16 + 18 - 16$ $\newline$ $y = (x^2 + 8x + 16) + 2$ $\newline$ Now, the equation includes the perfect square trinomial $(x^2 + 8x + 16)$ and the constant $2$ .
Factor and simplify: Factor the perfect square trinomial and simplify the equation. $\newline$ $y = (x + 4)^2 + 2$ $\newline$ This is the vertex form of the given parabola, where the vertex is $(-4, 2)$ .

More problems from Convert equations of parabolas from general to vertex form

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What is the focus of the parabola

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Simplify any fractions.

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Question

In which direction does the parabola

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\newline

\text{up}

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What is the vertex of the parabola

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?

\newline

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What is the axis of symmetry of the parabola

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

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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}

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What is the vertex of the parabola

y - 8x^2 = 4

\newline

(\_,\_)

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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

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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