The equation of a parabola is y = x^2 + 2x - 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 the Square: Complete the square to transform the given equation into vertex form. The given equation is y = x^2 + 2x - 4. 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. The value needed is (2/2)^2 = 1. We add and subtract 1 inside the equation.Add Value Found: Add and subtract the value found in Step 2 to the equation. y = x^2 + 2x - 4 y = x^2 + 2x + 1 - 1 - 4 Now, group the perfect square trinomial and the constants.Rewrite Equation: Rewrite the equation with the perfect square trinomial and combine the constants. y = (x^2 + 2x + 1) - 1 - 4 y = (x + 1)^2 - 5 Now, the equation is in vertex form, where the vertex is (-1, -5).

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The equation of a parabola is $y = x^2 + 2x - 4$ . 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 + 2x - 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 the Square: Complete the square to transform the given equation into vertex form. $\newline$ The given equation is $y = x^2 + 2x - 4$ . To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial with $x^2 + 2x$ . $\newline$ The value needed is $(2/2)^2 = 1$ . We add and subtract $1$ inside the equation.
Add Value Found: Add and subtract the value found in Step $2$ to the equation. $\newline$ $y = x^2 + 2x - 4$ $\newline$ $y = x^2 + 2x + 1 - 1 - 4$ $\newline$ Now, group the perfect square trinomial and the constants.
Rewrite Equation: Rewrite the equation with the perfect square trinomial and combine the constants. $\newline$ $y = (x^2 + 2x + 1) - 1 - 4$ $\newline$ $y = (x + 1)^2 - 5$ $\newline$ Now, the equation is in vertex form, where the vertex is $(-1, -5)$ .