The equation of a parabola is y = x^2 - 6x + 2. 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 transform the given equation into vertex form. The given equation is y = x^2 - 6x + 2. To complete the square, we need to find the value that makes x^2 - 6x 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 -6 is -3, and (-3)^2 = 9. So we add and subtract 9 from the right side of the equation. y = x^2 - 6x + 9 - 9 + 2Rewrite equation: Rewrite the equation with the perfect square trinomial and combine the constants. y = (x^2 - 6x + 9) - 9 + 2 y = (x - 3)^2 - 7 Now the equation is in vertex form, where (h, k) = (3, -7).

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The equation of a parabola is $y = x^2 - 6x + 2$ . 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 - 6x + 2

. 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 the square: Complete the square to transform the given equation into vertex form. $\newline$ The given equation is $y = x^2 - 6x + 2$ . To complete the square, we need to find the value that makes $x^2 - 6x$ 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 $-6$ is $-3$ , and $(-3)^2 = 9$ . So we add and subtract $9$ from the right side of the equation. $\newline$ $y = x^2 - 6x + 9 - 9 + 2$
Rewrite equation: Rewrite the equation with the perfect square trinomial and combine the constants. $\newline$ $y = (x^2 - 6x + 9) - 9 + 2$ $\newline$ $y = (x - 3)^2 - 7$ $\newline$ Now the equation is in vertex form, where $(h, k) = (3, -7)$ .