The equation of a parabola is y = x^2 + 8x + 25. 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 given equation in vertex form. We have the equation y = x^2 + 8x + 25. To complete the square, we need to find a value that makes x^2 + 8x a perfect square trinomial. We do this by taking half of the coefficient of x, squaring it, and adding it to and subtracting it from the equation. Half of 8 is 4, and 4 squared is 16. However, we notice that the constant term is already 25, which is a perfect square (5^2). This suggests that the equation may already be a perfect square trinomial.Verify Perfect Square: Verify if the given equation is already a perfect square trinomial. We can rewrite the equation as y = (x^2 + 8x + 16) + (25 - 16) to see if it forms a perfect square. y = (x + 4)^2 + 9 Since (x + 4)^2 is a perfect square trinomial, we have successfully written the equation in vertex form without needing to add and subtract a term.Write Final Equation: Write the final equation in vertex form. The equation in vertex form is y = (x + 4)^2 + 9.

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The equation of a parabola is $y = x^2 + 8x + 25$ . 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 + 25

. 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 given equation in vertex form. $\newline$ We have the equation $y = x^2 + 8x + 25$ . To complete the square, we need to find a value that makes $x^2 + 8x$ a perfect square trinomial. We do this by taking half of the coefficient of $x$ , squaring it, and adding it to and subtracting it from the equation. $\newline$ Half of $8$ is $4$ , and $4$ squared is $16$ . However, we notice that the constant term is already $25$ , which is a perfect square ( $5^2$ ). This suggests that the equation may already be a perfect square trinomial.
Verify Perfect Square: Verify if the given equation is already a perfect square trinomial. $\newline$ We can rewrite the equation as $y = (x^2 + 8x + 16) + (25 - 16)$ to see if it forms a perfect square. $\newline$ $y = (x + 4)^2 + 9$ $\newline$ Since $(x + 4)^2$ is a perfect square trinomial, we have successfully written the equation in vertex form without needing to add and subtract a term.
Write Final Equation: Write the final equation in vertex form. $\newline$ The equation in vertex form is $y = (x + 4)^2 + 9$ .