The equation of a parabola is y = x^2 - 4x + 12. 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. We have the equation y = x^2 - 4x + 12. To complete the square, we need to find the value that makes x^2 - 4x 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 the coefficient of x is -4/2 = -2. Squaring this gives us (-2)^2 = 4. We add and subtract 4 to the equation.Add/Subtract Squared Term: Add and subtract the squared term inside the equation. y = x^2 - 4x + 4 - 4 + 12 Now, group the perfect square trinomial and the constants. y = (x^2 - 4x + 4) - 4 + 12Factor and Simplify: Factor the perfect square trinomial and simplify the constants. y = (x - 2)^2 - 4 + 12 y = (x - 2)^2 + 8 Now we have the equation in vertex form, where the vertex is (2, 8).

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The equation of a parabola is $y = x^2 - 4x + 12$ . 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 + 12

. 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 transform the given equation into vertex form. $\newline$ We have the equation $y = x^2 - 4x + 12$ . To complete the square, we need to find the value that makes $x^2 - 4x$ 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 the coefficient of $x$ is $-4/2 = -2$ . Squaring this gives us $(-2)^2 = 4$ . We add and subtract $4$ to the equation.
Add/Subtract Squared Term: Add and subtract the squared term inside the equation. $\newline$ $y = x^2 - 4x + 4 - 4 + 12$ $\newline$ Now, group the perfect square trinomial and the constants. $\newline$ $y = (x^2 - 4x + 4) - 4 + 12$
Factor and Simplify: Factor the perfect square trinomial and simplify the constants. $\newline$ $y = (x - 2)^2 - 4 + 12$ $\newline$ $y = (x - 2)^2 + 8$ $\newline$ Now we have the equation in vertex form, where the vertex is $(2, 8)$ .