The equation of a parabola is y = x^2 + 8x + 26. 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 + 8x + 26. 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 + 8x. This number is (8/2)^2 = 4^2 = 16. We add and subtract 16 within the equation. y = x^2 + 8x + 16 + 26 - 16Rewrite and Simplify: Rewrite the equation with the perfect square trinomial and simplify. Now we have y = (x^2 + 8x + 16) + 26 - 16. The expression in the parentheses is a perfect square trinomial and can be written as (x + 4)^2. Simplifying the constants gives us: y = (x + 4)^2 + 10

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The equation of a parabola is $y = x^2 + 8x + 26$ . 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 + 8x + 26

. 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 $y = x^2 + 8x + 26$ . To complete the square, we need to find a number that, when added and subtracted to the equation, forms a perfect square trinomial with $x^2 + 8x$ . This number is $(8/2)^2 = 4^2 = 16$ . We add and subtract $16$ within the equation. $\newline$ $y = x^2 + 8x + 16 + 26 - 16$
Rewrite and Simplify: Rewrite the equation with the perfect square trinomial and simplify. $\newline$ Now we have $y = (x^2 + 8x + 16) + 26 - 16$ . The expression in the parentheses is a perfect square trinomial and can be written as $(x + 4)^2$ . Simplifying the constants gives us: $\newline$ $y = (x + 4)^2 + 10$