The equation of a parabola is y = x^2 + 4x + 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 Square: Complete the square to transform the given equation into vertex form. We have the equation y = x^2 + 4x + 7. 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/Subtract Value: Add and subtract the value found in Step 2 to the equation. y = x^2 + 4x + 7 y = x^2 + 4x + 4 - 4 + 7 We added and subtracted 4 to complete the square without changing the equation's value.Rewrite Equation: Rewrite the equation grouping the perfect square trinomial and combining the constants. y = (x^2 + 4x + 4) - 4 + 7 y = (x + 2)^2 + 3 Now the equation is in vertex form, where (x + 2)^2 is the perfect square trinomial and 3 is the combined constant.

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The equation of a parabola is $y = x^2 + 4x + 7$ . 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 + 4x + 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. 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 $y = x^2 + 4x + 7$ . 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/Subtract Value: Add and subtract the value found in Step $2$ to the equation. $\newline$ $y = x^2 + 4x + 7$ $\newline$ $y = x^2 + 4x + 4 - 4 + 7$ $\newline$ We added and subtracted $4$ to complete the square without changing the equation's value.
Rewrite Equation: Rewrite the equation grouping the perfect square trinomial and combining the constants. $\newline$ $y = (x^2 + 4x + 4) - 4 + 7$ $\newline$ $y = (x + 2)^2 + 3$ $\newline$ Now the equation is in vertex form, where $(x + 2)^2$ is the perfect square trinomial and $3$ is the combined constant.