The equation of a parabola is y = x^2 + 4x + 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 y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.Complete square: Complete the square to transform the given equation into vertex form. We have the equation y = x^2 + 4x + 2. To complete the square, we need to find the value that makes x^2 + 4x a perfect square trinomial. This value is (4/2)^2 = 2^2 = 4. We will add and subtract this value inside the equation.Add and subtract: Add and subtract the value found in Step 2 to the equation. y = x^2 + 4x + 4 - 4 + 2 Now, we have added 4 and subtracted 4, which keeps the equation balanced.Rewrite equation: Rewrite the equation grouping the perfect square trinomial and combining the constants. y = (x^2 + 4x + 4) - 4 + 2 y = (x + 2)^2 - 2 Now, the equation is in the vertex form y = a(x - h)^2 + k, where a = 1, h = -2, and k = -2.

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The equation of a parabola is $y = x^2 + 4x + 2$ . 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 + 4x + 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 $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Complete square: Complete the square to transform the given equation into vertex form. $\newline$ We have the equation $y = x^2 + 4x + 2$ . To complete the square, we need to find the value that makes $x^2 + 4x$ a perfect square trinomial. This value is $(4/2)^2 = 2^2 = 4$ . We will add and subtract this value inside the equation.
Add and subtract: Add and subtract the value found in Step $2$ to the equation. $\newline$ $y = x^2 + 4x + 4 - 4 + 2$ $\newline$ Now, we have added $4$ and subtracted $4$ , which keeps the equation balanced.
Rewrite equation: Rewrite the equation grouping the perfect square trinomial and combining the constants. $\newline$ $y = (x^2 + 4x + 4) - 4 + 2$ $\newline$ $y = (x + 2)^2 - 2$ $\newline$ Now, the equation is in the vertex form $y = a(x - h)^2 + k$ , where $a = 1$ , $h = -2$ , and $k = -2$ .