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Complete the square to re-write the quadratic function in vertex form:

y=x^(2)+8x+9
Answer:
y=

Complete the square to re-write the quadratic function in vertex form: $\newline$ $y=x^{2}+8 x+9$ $\newline$ Answer: $y=$

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Convert equations of parabolas from general to vertex form

Full solution

Q. Complete the square to re-write the quadratic function in vertex form:

\newline

y=x^{2}+8 x+9

\newline

Answer:

y=

Identify Vertex Form: Identify the vertex form of a parabola. $\newline$ The vertex form of a parabola is $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Begin with Quadratic Function: Begin with the given quadratic function. $\newline$ We have $y = x^2 + 8x + 9$ .
Find Constant to Complete: Find the constant to complete the square. $\newline$ To complete the square, we need to add and subtract the square of half the coefficient of $x$ . The coefficient of $x$ is $8$ , so half of it is $4$ , and the square of $4$ is $16$ .
Add and Subtract Constant: Add and subtract the constant inside the equation. $\newline$ We add and subtract $16$ inside the equation to complete the square. $\newline$ $y = x^2 + 8x + 16 - 16 + 9$
Group and Combine: Group the perfect square trinomial and combine the constants. $\newline$ $y = (x^2 + 8x + 16) - 7$ $\newline$ Now, we can write the perfect square trinomial as a square of a binomial. $\newline$ $y = (x + 4)^2 - 7$
Write in Vertex Form: Write the equation in vertex form. $\newline$ The vertex form of the equation is $y = (x + 4)^2 - 7$ .

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}

\newline

\text{down}

\newline

\text{right}

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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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Question

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

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(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