The equation of a parabola is y = x^2 + 4x + 14. 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 + 14. 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 + 14 y = x^2 + 4x + 4 - 4 + 14 We added and subtracted 4 to complete the square, and we have not changed the equation because adding and subtracting the same number is equivalent to adding zero.Rewrite equation: Rewrite the equation by grouping the perfect square trinomial and combining the constants. y = (x^2 + 4x + 4) - 4 + 14 y = (x + 2)^2 + 10 Now the equation is in vertex form, where (x + 2)^2 is the perfect square trinomial and 10 is the combined constant.

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The equation of a parabola is $y = x^2 + 4x + 14$ . 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 + 14

. 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 $y = x^2 + 4x + 14$ . 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. $\newline$ $y = x^2 + 4x + 14$ $\newline$ $y = x^2 + 4x + 4 - 4 + 14$ $\newline$ We added and subtracted $4$ to complete the square, and we have not changed the equation because adding and subtracting the same number is equivalent to adding zero.
Rewrite equation: Rewrite the equation by grouping the perfect square trinomial and combining the constants. $\newline$ $y = (x^2 + 4x + 4) - 4 + 14$ $\newline$ $y = (x + 2)^2 + 10$ $\newline$ Now the equation is in vertex form, where $(x + 2)^2$ is the perfect square trinomial and $10$ is the combined constant.