The equation of a parabola is y = x^2 - 2x + 8. 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 transform the given equation into vertex form. The given equation is y = x^2 - 2x + 8. To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial with x^2 - 2x. The value needed is (2/2)^2 = 1. We add and subtract 1 inside the equation.Add value: Add and subtract the value found in Step 2 to the equation. y = x^2 - 2x + 1 + 8 - 1 This step creates a perfect square trinomial and maintains the equality by adding and subtracting the same value.Rewrite equation: Rewrite the equation with the perfect square trinomial and combine like terms. y = (x^2 - 2x + 1) + 8 - 1 y = (x - 1)^2 + 7 Now the equation is in vertex form, where (x - 1)^2 is the perfect square trinomial and + 7 is the combination of the constants.

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

. 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 transform the given equation into vertex form. $\newline$ The given equation is $y = x^2 - 2x + 8$ . To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial with $x^2 - 2x$ . The value needed is $(2/2)^2 = 1$ . We add and subtract $1$ inside the equation.
Add value: Add and subtract the value found in Step $2$ to the equation. $\newline$ $y = x^2 - 2x + 1 + 8 - 1$ $\newline$ This step creates a perfect square trinomial and maintains the equality by adding and subtracting the same value.
Rewrite equation: Rewrite the equation with the perfect square trinomial and combine like terms. $\newline$ $y = (x^2 - 2x + 1) + 8 - 1$ $\newline$ $y = (x - 1)^2 + 7$ $\newline$ Now the equation is in vertex form, where $(x - 1)^2$ is the perfect square trinomial and $+ 7$ is the combination of the constants.