The equation of a parabola is y = x^2 + 2x - 3. 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 rewrite the equation y = x^2 + 2x - 3 in vertex form. First, we need to complete the square for the x-terms. To do this, we take half of the coefficient of x, which is 2, divide it by 2 to get 1, and then square it to get 1. We will add and subtract this value inside the equation.Add/subtract square: Add and subtract the square of half the coefficient of x inside the equation. The equation becomes y = x^2 + 2x + 1 - 1 - 3. We added 1 and subtracted 1 to complete the square without changing the equation's value.Group trinomial, combine: Group the perfect square trinomial and combine the constants. The equation now is y = (x^2 + 2x + 1) - 1 - 3. The perfect square trinomial is (x + 1)^2, and combining the constants -1 and -3 gives us -4.Write in vertex form: Write the equation in vertex form. The equation in vertex form is y = (x + 1)^2 - 4.

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The equation of a parabola is $y = x^2 + 2x - 3$ . 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 - 3

. 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 rewrite the equation $y = x^2 + 2x - 3$ in vertex form. $\newline$ First, we need to complete the square for the $x$ -terms. To do this, we take half of the coefficient of $x$ , which is $2$ , divide it by $2$ to get $1$ , and then square it to get $1$ . We will add and subtract this value inside the equation.
Add/subtract square: Add and subtract the square of half the coefficient of $x$ inside the equation. $\newline$ The equation becomes $y = x^2 + 2x + 1 - 1 - 3$ . $\newline$ We added $1$ and subtracted $1$ to complete the square without changing the equation's value.
Group trinomial, combine: Group the perfect square trinomial and combine the constants. $\newline$ The equation now is $y = (x^2 + 2x + 1) - 1 - 3$ . $\newline$ The perfect square trinomial is $(x + 1)^2$ , and combining the constants $-1$ and $-3$ gives us $-4$ .
Write in vertex form: Write the equation in vertex form. $\newline$ The equation in vertex form is $y = (x + 1)^2 - 4$ .