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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

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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 $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Consider given equation: Consider the given equation $y = x^2 - 8x + 18$ . $\newline$ We need to complete the square to rewrite this equation in vertex form.
Find square of half: Find the square of half the coefficient of $x$ . Half the coefficient of $x$ is $-8/2$ , which is $-4$ . Squaring this gives us $(-4)^2 = 16$ .
Add and subtract square: Add and subtract the square of half the coefficient of $x$ inside the equation. $\newline$ $y = x^2 - 8x + 16 - 16 + 18$ $\newline$ We add and subtract $16$ to complete the square while keeping the equation balanced.
Rewrite equation by grouping: Rewrite the equation by grouping the perfect square trinomial and combining the constants. $\newline$ $y = (x^2 - 8x + 16) - 16 + 18$ $\newline$ $y = (x - 4)^2 + 2$ $\newline$ Now the equation is in vertex form, where $(h, k) = (4, 2)$ .

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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

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and the radius is

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(C) The center is

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Question

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

\newline

The given equation is graphed in the

x y

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x

-intercepts of the graph?

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1

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-3

-9

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-3

9

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3

-9

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3

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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

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x

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y

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x

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y

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