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The equation of a parabola is $y = x^2 - 8x + 17$ . 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 + 17

. 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. The vertex form of a parabola is given by $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Given Quadratic Equation: Consider the given quadratic equation $y = x^2 - 8x + 17$ . $\newline$ We need to complete the square to transform this equation into vertex form.
Find Square of Half: Find the square of half the coefficient of $x$ . The coefficient of $x$ is $-8$ . Half of this coefficient is $-8/2 = -4$ . Squaring this value gives $(-4)^2 = 16$ .
Rewrite Quadratic Equation: Rewrite the quadratic equation by adding and subtracting the square of half the coefficient of $x$ . $y = x^2 - 8x + 16 + 17 - 16$ $y = (x^2 - 8x + 16) + 1$
Recognize Perfect Square Trinomial: Recognize the perfect square trinomial and factor it. $\newline$ $y = (x - 4)^2 + 1$ $\newline$ This is now in vertex form, where $(h, k) = (4, 1)$ .

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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

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(C) The center 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

-plane. Which of the following are

x

-intercepts of the graph?

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1

\newline

-3

-9

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-3

9

\newline

3

-9

\newline

3

9

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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

\newline

x

\newline

y

\newline

x

-coordinate of the vertex

\newline

y

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