The equation of a parabola is y = x^2 + 10x + 21. 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 rewrite the equation in vertex form. We have the equation y = x^2 + 10x + 21. To complete the square, we need to find the value that makes x^2 + 10x into a perfect square trinomial. This value is (10/2)^2 = 25. We will add and subtract 25 inside the equation.Add and Subtract 25: Add and subtract 25 to the equation. y = x^2 + 10x + 21 y = x^2 + 10x + 25 + 21 - 25 We added 25 to form a perfect square trinomial and subtracted 25 to keep the equation balanced.Factor and Simplify: Factor the perfect square trinomial and simplify. y = (x^2 + 10x + 25) + 21 - 25 y = (x + 5)^2 + 21 - 25 y = (x + 5)^2 - 4 Now the equation is in vertex form, where (h, k) = (-5, -4).

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The equation of a parabola is $y = x^2 + 10x + 21$ . 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 + 10x + 21

. 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 rewrite the equation in vertex form. $\newline$ We have the equation $y = x^2 + 10x + 21$ . To complete the square, we need to find the value that makes $x^2 + 10x$ into a perfect square trinomial. This value is $(10/2)^2 = 25$ . We will add and subtract $25$ inside the equation.
Add and Subtract $25$ : Add and subtract $25$ to the equation. $\newline$ $y = x^2 + 10x + 21$ $\newline$ $y = x^2 + 10x + 25 + 21 - 25$ $\newline$ We added $25$ to form a perfect square trinomial and subtracted $25$ to keep the equation balanced.
Factor and Simplify: Factor the perfect square trinomial and simplify. $\newline$ $y = (x^2 + 10x + 25) + 21 - 25$ $\newline$ $y = (x + 5)^2 + 21 - 25$ $\newline$ $y = (x + 5)^2 - 4$ $\newline$ Now the equation is in vertex form, where $(h, k) = (-5, -4)$ .