The equation of a parabola is y = x^2 - 2x - 6. 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, which is y = a(x - h)^2 + k.Complete the Square: Start with the given equation y = x^2 - 2x - 6. To complete the square, calculate (2/2)^2 = 1 and add & subtract 1 inside the equation.Rewrite Equation: Rewrite the equation as y = x^2 - 2x + 1 - 1 - 6. Group the perfect square trinomial and the constants.Factor Trinomial: Now, y = (x^2 - 2x + 1) - 1 - 6. Factor the trinomial to get (x - 1)^2.Combine Constants: Combine the constants to get -7. So, y = (x - 1)^2 - 7. This is the vertex form of the parabola.

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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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Algebra 1

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, which is $y = a(x - h)^2 + k$ .
Complete the Square: Start with the given equation $y = x^2 - 2x - 6$ . $\newline$ To complete the square, calculate $(2/2)^2 = 1$ and add & subtract $1$ inside the equation.
Rewrite Equation: Rewrite the equation as $y = x^2 - 2x + 1 - 1 - 6$ . Group the perfect square trinomial and the constants.
Factor Trinomial: Now, $y = (x^2 - 2x + 1) - 1 - 6$ . Factor the trinomial to get $(x - 1)^2$ .
Combine Constants: Combine the constants to get $-7$ . $\newline$ So, $y = (x - 1)^2 - 7$ . $\newline$ This is the vertex form of the parabola.