The equation of a parabola is y = x^2 - 4x + 7. 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 the square: Complete the square to rewrite the given equation in vertex form. We have the equation y = x^2 - 4x + 7. 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 -4 is -2, and (-2)^2 = 4. So we add and subtract 4 to the equation.Add squared number: Add and subtract the squared number to the equation. y = x^2 - 4x + 4 + 7 - 4 Now we have added 4 and subtracted 4, which keeps the equation balanced.Group and combine: Group the perfect square trinomial and combine the constants. y = (x^2 - 4x + 4) + 7 - 4 y = (x - 2)^2 + 3 Now we have the equation in vertex form, where (x - 2)^2 is the perfect square trinomial and 3 is the combined constant.

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The equation of a parabola is $y = x^2 - 4x + 7$ . 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 + 7

. 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 the square: Complete the square to rewrite the given equation in vertex form. $\newline$ We have the equation $y = x^2 - 4x + 7$ . 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 $-4$ is $-2$ , and $(-2)^2 = 4$ . So we add and subtract $4$ to the equation.
Add squared number: Add and subtract the squared number to the equation. $\newline$ $y = x^2 - 4x + 4 + 7 - 4$ $\newline$ Now we have added $4$ and subtracted $4$ , which keeps the equation balanced.
Group and combine: Group the perfect square trinomial and combine the constants. $\newline$ $y = (x^2 - 4x + 4) + 7 - 4$ $\newline$ $y = (x - 2)^2 + 3$ $\newline$ Now we have the equation in vertex form, where $(x - 2)^2$ is the perfect square trinomial and $3$ is the combined constant.