The equation of a parabola is y = x^2 - 4x - 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. 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 square: Complete the square to rewrite the given equation in vertex form. We start with the given equation y = x^2 - 4x - 6. To complete the square, we need to find a number that, when added and subtracted to the equation, forms a perfect square trinomial with x^2 - 4x. This number is (4/2)^2 = 4. We add and subtract 4 inside the equation. y = x^2 - 4x + 4 - 4 - 6Rewrite equation: Rewrite the equation to show the perfect square trinomial. Now we group the perfect square trinomial and combine the constants: y = (x^2 - 4x + 4) - 4 - 6 y = (x - 2)^2 - 10Verify form: Verify the vertex form and check for any mathematical errors. The equation is now in vertex form, y = a(x - h)^2 + k, where a = 1, h = 2, and k = -10. There are no mathematical errors in the steps taken to complete the square and rewrite the equation.

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The equation of a parabola is $y = x^2 - 4x - 6$ . 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 - 4x - 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. $\newline$ 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 square: Complete the square to rewrite the given equation in vertex form. $\newline$ We start with the given equation $y = x^2 - 4x - 6$ . To complete the square, we need to find a number that, when added and subtracted to the equation, forms a perfect square trinomial with $x^2 - 4x$ . This number is $(\frac{4}{2})^2 = 4$ . We add and subtract $4$ inside the equation. $\newline$ $y = x^2 - 4x + 4 - 4 - 6$
Rewrite equation: Rewrite the equation to show the perfect square trinomial. $\newline$ Now we group the perfect square trinomial and combine the constants: $\newline$ $y = (x^2 - 4x + 4) - 4 - 6$ $\newline$ $y = (x - 2)^2 - 10$
Verify form: Verify the vertex form and check for any mathematical errors. $\newline$ The equation is now in vertex form, $y = a(x - h)^2 + k$ , where $a = 1$ , $h = 2$ , and $k = -10$ . There are no mathematical errors in the steps taken to complete the square and rewrite the equation.