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The equation of a parabola is $y = x^2 + 6x + 19$ . 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 + 6x + 19

. 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.
Complete the square: Complete the square to rewrite the given equation in vertex form. $\newline$ The given equation is $y = x^2 + 6x + 19$ . To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial.
Calculate value: Calculate the value needed to complete the square. $\newline$ We take the coefficient of the $x$ term, which is $6$ , divide it by $2$ , and then square it to get the value to add and subtract. $\newline$ $(\frac{6}{2})^2 = 3^2 = 9$
Add and subtract: Add and subtract the calculated value inside the equation. $\newline$ $y = x^2 + 6x + 9 + 19 - 9$ $\newline$ $y = (x^2 + 6x + 9) + 10$ $\newline$ Now, the equation has a perfect square trinomial and a constant term $10$ .
Factor and simplify: Factor the perfect square trinomial and simplify the equation. $\newline$ $y = (x + 3)^2 + 10$ $\newline$ This is the equation in vertex form, where the vertex is $(-3, 10)$ .

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Question

The equation of a circle is

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\newline

1

\newline

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and the radius is

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(B) The center is

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

\newline

The given equation is graphed in the

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x

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1

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-3

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-3

9

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3

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Question

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is graphed in the

x y

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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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