The equation of a parabola is y = x^2 + 2x - 9. 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 y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.Complete Square: Complete the square to rewrite the equation y = x^2 + 2x - 9 in vertex form. First, we need to complete the square for the x-terms. To do this, we take the coefficient of x, which is 2, divide it by 2, and square it. This gives us (2/2)^2 = 1^2 = 1. We will add and subtract this value inside the equation.Add/Subtract Value: Add and subtract the value found in Step 2 inside the equation. y = x^2 + 2x + 1 - 1 - 9 Now, we have added 1 and subtracted 1, which keeps the equation balanced.Group Perfect Square: Group the perfect square trinomial and combine the constants. y = (x^2 + 2x + 1) - 1 - 9 y = (x + 1)^2 - 10 We have now written the equation in vertex form, where (x + 1)^2 is the perfect square trinomial and -10 is the combination of the constants.

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The equation of a parabola is $y = x^2 + 2x - 9$ . 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 - 9

. 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 $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Complete Square: Complete the square to rewrite the equation $y = x^2 + 2x - 9$ in vertex form. $\newline$ First, we need to complete the square for the $x$ -terms. To do this, we take the coefficient of $x$ , which is $2$ , divide it by $2$ , and square it. This gives us $(2/2)^2 = 1^2 = 1$ . We will add and subtract this value inside the equation.
Add/Subtract Value: Add and subtract the value found in Step $2$ inside the equation. $\newline$ $y = x^2 + 2x + 1 - 1 - 9$ $\newline$ Now, we have added $1$ and subtracted $1$ , which keeps the equation balanced.
Group Perfect Square: Group the perfect square trinomial and combine the constants. $\newline$ $y = (x^2 + 2x + 1) - 1 - 9$ $\newline$ $y = (x + 1)^2 - 10$ $\newline$ We have now written the equation in vertex form, where $(x + 1)^2$ is the perfect square trinomial and $-10$ is the combination of the constants.