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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. The vertex form of a parabola is given by $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Begin with Quadratic Function: Begin with the given quadratic function. $\newline$ We have the quadratic function $y = x^2 + 8x - 9$ .
Separate Constant Term: Separate the constant term from the $x$ terms. $\newline$ To complete the square, we need to isolate the $x$ terms. So we write the function as $y = (x^2 + 8x) - 9$ .
Find Completing Number: Find the number to complete the square. $\newline$ To complete the square, we need to add and subtract the square of half the coefficient of $x$ inside the parentheses. The coefficient of $x$ is $8$ , so half of it is $4$ , and the square of $4$ is $16$ . We will add and subtract $16$ inside the parentheses.
Add/Subtract Square: Add and subtract the square of half the coefficient of $x$ inside the parentheses. $\newline$ We write the function as $y = (x^2 + 8x + 16) - 16 - 9$ .
Factor and Simplify: Factor the perfect square trinomial and simplify the constants. $\newline$ The expression $x^2 + 8x + 16$ is a perfect square trinomial and can be factored as $(x + 4)^2$ . The constants $-16$ and $-9$ combine to $-25$ . So the function becomes $y = (x + 4)^2 - 25$ .
Write Final Vertex Form: Write the final vertex form of the quadratic function. $\newline$ The vertex form of the quadratic function is $y = (x + 4)^2 - 25$ .

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Question

The equation of a circle is

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. What are the center and radius of the circle?

\newline

1

\newline

(A) The center is

(-4,0)

and the radius is

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(B) The center is

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and the radius is

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(D) The center 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

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x

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1

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-3

-9

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-3

9

\newline

3

-9

\newline

3

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Question

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

is graphed in the

x y

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\newline

1

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x

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y

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x

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y

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