The equation of a parabola is y = x^2 - 10x + 27. 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 the equation 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 start with the given equation y = x^2 - 10x + 27. To complete the square, we need to find the value that makes x^2 - 10x a perfect square trinomial. This value is given by (b/2)^2, where b is the coefficient of x. In this case, b = -10, so (b/2)^2 = (-10/2)^2 = (-5)^2 = 25. We will add and subtract this value inside the equation.Add and Subtract Value: Add and subtract the value found in Step 2 to the equation. y = x^2 - 10x + 25 + 27 - 25 This allows us to write the equation as a perfect square trinomial plus a constant.Factor and Simplify: Factor the perfect square trinomial and simplify the constants. y = (x^2 - 10x + 25) + 27 - 25 y = (x - 5)^2 + 2 Now the equation is in vertex form, where (h, k) = (5, 2).

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The equation of a parabola is $y = x^2 - 10x + 27$ . 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 + 27

. 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 the equation $y = a(x - h)^2 + k$ , 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 start with the given equation $y = x^2 - 10x + 27$ . To complete the square, we need to find the value that makes $x^2 - 10x$ a perfect square trinomial. This value is given by $(b/2)^2$ , where $b$ is the coefficient of $x$ . In this case, $b = -10$ , so $(b/2)^2 = (-10/2)^2 = (-5)^2 = 25$ . We will add and subtract this value inside the equation.
Add and Subtract Value: Add and subtract the value found in Step $2$ to the equation. $\newline$ $y = x^2 - 10x + 25 + 27 - 25$ $\newline$ This allows us to write the equation as a perfect square trinomial plus a constant.
Factor and Simplify: Factor the perfect square trinomial and simplify the constants. $\newline$ $y = (x^2 - 10x + 25) + 27 - 25$ $\newline$ $y = (x - 5)^2 + 2$ $\newline$ Now the equation is in vertex form, where $(h, k) = (5, 2)$ .