The equation of a parabola is y = x^2 + 4x - 4. 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 Transformation: Complete the square to transform the given equation into vertex form. We have the equation y = x^2 + 4x - 4. To complete the square, we need to find a number that, when added and subtracted to the equation, forms a perfect square trinomial with x^2 + 4x. This number is (4/2)^2 = 2^2 = 4. We add and subtract 4 within the equation.Add and Subtract Number: Add and subtract the number found in Step 2 to the equation. y = x^2 + 4x + 4 - 4 - 4 Now we have added 4 and subtracted 4, keeping the equation balanced.Rewrite Equation: Rewrite the equation grouping the perfect square trinomial and combining the constants. y = (x^2 + 4x + 4) - 8 Now we have a perfect square trinomial and a constant.Factor Perfect Square Trinomial: Factor the perfect square trinomial. y = (x + 2)^2 - 8 The factored form of x^2 + 4x + 4 is (x + 2)^2, and we bring down the constant -8.Final Equation: Write the final equation in vertex form. The equation in vertex form is y = (x + 2)^2 - 8.

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

. 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 Transformation: Complete the square to transform the given equation into vertex form. $\newline$ We have the equation $y = x^2 + 4x - 4$ . To complete the square, we need to find a number that, when added and subtracted to the equation, forms a perfect square trinomial with $x^2 + 4x$ . This number is $(4/2)^2 = 2^2 = 4$ . We add and subtract $4$ within the equation.
Add and Subtract Number: Add and subtract the number found in Step $2$ to the equation. $\newline$ $y = x^2 + 4x + 4 - 4 - 4$ $\newline$ Now we have added $4$ and subtracted $4$ , keeping the equation balanced.
Rewrite Equation: Rewrite the equation grouping the perfect square trinomial and combining the constants. $\newline$ $y = (x^2 + 4x + 4) - 8$ $\newline$ Now we have a perfect square trinomial and a constant.
Factor Perfect Square Trinomial: Factor the perfect square trinomial. $\newline$ $y = (x + 2)^2 - 8$ $\newline$ The factored form of $x^2 + 4x + 4$ is $(x + 2)^2$ , and we bring down the constant $-8$ .
Final Equation: Write the final equation in vertex form. $\newline$ The equation in vertex form is $y = (x + 2)^2 - 8$ .