The equation of a parabola is y = x^2 - 4x - 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 Square Transformation: Complete the square to transform the given equation into vertex form. Start with the given equation: y = x^2 - 4x - 2. 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. The value to add and subtract is (4/2)^2 = 2^2 = 4. Add and subtract 4 within the equation: y = x^2 - 4x + 4 - 4 - 2.Rewrite Equation with Trinomial: Rewrite the equation with the perfect square trinomial and the constants grouped together. The equation now looks like this: y = (x^2 - 4x + 4) - 4 - 2. Factor the perfect square trinomial: y = (x - 2)^2 - 4 - 2. Combine the constants: y = (x - 2)^2 - 6.Final Equation in Vertex Form: Write the final equation in vertex form. The equation in vertex form is y = (x - 2)^2 - 6.

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The equation of a parabola is $y = x^2 - 4x - 2$ . 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 - 4x - 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. 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 Transformation: Complete the square to transform the given equation into vertex form. $\newline$ Start with the given equation: $y = x^2 - 4x - 2$ . $\newline$ 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 value to add and subtract is $(4/2)^2 = 2^2 = 4$ . $\newline$ Add and subtract $4$ within the equation: $y = x^2 - 4x + 4 - 4 - 2$ .
Rewrite Equation with Trinomial: Rewrite the equation with the perfect square trinomial and the constants grouped together. $\newline$ The equation now looks like this: $y = (x^2 - 4x + 4) - 4 - 2$ . $\newline$ Factor the perfect square trinomial: $y = (x - 2)^2 - 4 - 2$ . $\newline$ Combine the constants: $y = (x - 2)^2 - 6$ .
Final Equation in Vertex Form: Write the final equation in vertex form. $\newline$ The equation in vertex form is $y = (x - 2)^2 - 6$ .