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The equation of a parabola is $y = x^2 - 2x + 6$ . Write the equation in vertex form. $\newline$ Write any numbers as integers or simplified proper or improper fractions. $\newline$ ______

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Write a quadratic function in vertex form

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Q. The equation of a parabola is

y = x^2 - 2x + 6

. 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 $y = x^2 - 2x + 6$ . To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial with the $x$ -terms. $\newline$ The coefficient of $x$ is $-2$ , so we take half of $-2$ , which is $-1$ , and then square it to get $1$ . We will add and subtract this value inside the equation.
Add Value Inside Equation: Add and subtract the value found in Step $2$ inside the equation. $\newline$ $y = x^2 - 2x + 1 + 6 - 1$ $\newline$ We added and subtracted $1$ to create a perfect square trinomial.
Rewrite Equation: Rewrite the equation with the perfect square trinomial and combine the constants. $\newline$ $y = (x^2 - 2x + 1) + 6 - 1$ $\newline$ $y = (x - 1)^2 + 5$ $\newline$ Now the equation is in vertex form, with the vertex at $(1, 5)$ .

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