The equation of a parabola is y = x^2 + 2x - 7. Write the equation in vertex form. Write any numbers as integers or simplified proper or improper fractions. ______

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.Complete the square: Complete the square to transform the given equation into vertex form. The given equation is y = x^2 + 2x - 7. 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 2, so half of it is 1, and squaring it gives us 1. We add and subtract 1 to complete the square. y = x^2 + 2x + 1 - 1 - 7Rewrite equation: Rewrite the equation by grouping the perfect square trinomial and combining the constants. y = (x^2 + 2x + 1) - 1 - 7 y = (x + 1)^2 - 8 Now, the equation is in vertex form, where (h, k) = (-1, -8).

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The equation of a parabola is $y = x^2 + 2x - 7$ . Write the equation in vertex form. $\newline$ Write any numbers as integers or simplified proper or improper fractions. $\newline$ ______

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Algebra 1

Write a quadratic function in vertex form

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Q. The equation of a parabola is

y = x^2 + 2x - 7

. 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 transform the given equation into vertex form. $\newline$ The given equation is $y = x^2 + 2x - 7$ . To complete the square, we need to add and subtract the square of half the coefficient of $x$ inside the parentheses. $\newline$ The coefficient of $x$ is $2$ , so half of it is $1$ , and squaring it gives us $1$ . We add and subtract $1$ to complete the square. $\newline$ $y = x^2 + 2x + 1 - 1 - 7$
Rewrite equation: Rewrite the equation by grouping the perfect square trinomial and combining the constants. $\newline$ $y = (x^2 + 2x + 1) - 1 - 7$ $\newline$ $y = (x + 1)^2 - 8$ $\newline$ Now, the equation is in vertex form, where $(h, k) = (-1, -8)$ .