The equation of a parabola is y = x^2 - 2x - 5. 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 rewrite the equation y = x^2 - 2x - 5 in vertex form. First, we need to complete the square for the x-terms. To do this, we take the coefficient of the x-term, divide it by 2, and square it. For the equation y = x^2 - 2x - 5, the coefficient of x is -2. Dividing it by 2 gives us -1, and squaring it gives us 1. We will add and subtract this value inside the equation.Add Square Value: Add and subtract the square of half the x-coefficient inside the equation. We have y = x^2 - 2x + 1 - 1 - 5. We added and subtracted 1 to complete the square.Group and Combine: Group the perfect square trinomial and combine the constants. Now we group the terms to form a perfect square trinomial and combine the constants: y = (x^2 - 2x + 1) - 1 - 5, which simplifies to y = (x - 1)^2 - 6.Write in Vertex Form: Write the equation in vertex form. The equation in vertex form is y = (x - 1)^2 - 6. This is the vertex form of the given parabola, where the vertex is (1, -6).

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The equation of a parabola is $y = x^2 - 2x - 5$ . 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 - 5

. 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 $y = x^2 - 2x - 5$ in vertex form. $\newline$ First, we need to complete the square for the $x$ -terms. To do this, we take the coefficient of the $x$ -term, divide it by $2$ , and square it. For the equation $y = x^2 - 2x - 5$ , the coefficient of $x$ is $-2$ . Dividing it by $2$ gives us $-1$ , and squaring it gives us $1$ . We will add and subtract this value inside the equation.
Add Square Value: Add and subtract the square of half the $x$ -coefficient inside the equation. $\newline$ We have $y = x^2 - 2x + 1 - 1 - 5$ . We added and subtracted $1$ to complete the square.
Group and Combine: Group the perfect square trinomial and combine the constants. $\newline$ Now we group the terms to form a perfect square trinomial and combine the constants: $y = (x^2 - 2x + 1) - 1 - 5$ , which simplifies to $y = (x - 1)^2 - 6$ .
Write in Vertex Form: Write the equation in vertex form. $\newline$ The equation in vertex form is $y = (x - 1)^2 - 6$ . This is the vertex form of the given parabola, where the vertex is $(1, -6)$ .