The equation of a parabola is y = x^2 + 2x + 2. 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 the equation 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. We start with the given equation y = x^2 + 2x + 2. To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial with x^2 + 2x. This value is (2/2)^2 = 1. We add and subtract 1 within the equation. y = x^2 + 2x + 1 + 2 - 1Highlight Perfect Trinomial: Rewrite the equation to highlight the perfect square trinomial. Now we group the perfect square trinomial and combine the constants: y = (x^2 + 2x + 1) + 2 - 1 y = (x + 1)^2 + 1Write in Vertex Form: Write the equation in vertex form. The equation is now in vertex form, which is y = a(x - h)^2 + k. Comparing this to our result, we have a = 1, h = -1, and k = 1. So the vertex form of the given parabola is: y = (x + 1)^2 + 1

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

. 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 the equation $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Complete the Square: Complete the square to rewrite the given equation in vertex form. $\newline$ We start with the given equation $y = x^2 + 2x + 2$ . To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial with $x^2 + 2x$ . This value is $(2/2)^2 = 1$ . We add and subtract $1$ within the equation. $\newline$ $y = x^2 + 2x + 1 + 2 - 1$
Highlight Perfect Trinomial: Rewrite the equation to highlight the perfect square trinomial. $\newline$ Now we group the perfect square trinomial and combine the constants: $\newline$ $y = (x^2 + 2x + 1) + 2 - 1$ $\newline$ $y = (x + 1)^2 + 1$
Write in Vertex Form: Write the equation in vertex form. $\newline$ The equation is now in vertex form, which is $y = a(x - h)^2 + k$ . Comparing this to our result, we have $a = 1$ , $h = -1$ , and $k = 1$ . So the vertex form of the given parabola is: $\newline$ $y = (x + 1)^2 + 1$