The equation of a parabola is y = x^2 - 4x - 1. 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: Complete the square to transform the given equation into vertex form. We have the equation y = x^2 - 4x - 1. 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. This value is found by taking half of the coefficient of x, squaring it, and then adding and subtracting it from the equation. Half of the coefficient of x is -4/2 = -2. Squaring this gives us (-2)^2 = 4. We will add and subtract 4 to the equation.Add value: Add and subtract the value found in Step 2 to the equation. y = x^2 - 4x + 4 - 4 - 1 Now we have added 4 and subtracted 4, which keeps the equation balanced.Rewrite equation: Rewrite the equation by grouping the perfect square trinomial and combining the constants. y = (x^2 - 4x + 4) - 4 - 1 y = (x - 2)^2 - 5 We have now written the equation in vertex form, where (x - 2)^2 is the perfect square trinomial and -5 is the combination of the constants.

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The equation of a parabola is $y = x^2 - 4x - 1$ . 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 - 1

. 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 $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Complete square: Complete the square to transform the given equation into vertex form. $\newline$ We have the equation $y = x^2 - 4x - 1$ . 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. This value is found by taking half of the coefficient of $x$ , squaring it, and then adding 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 will add and subtract $4$ to the equation.
Add value: Add and subtract the value found in Step $2$ to the equation. $\newline$ $y = x^2 - 4x + 4 - 4 - 1$ $\newline$ Now we have added $4$ and subtracted $4$ , which keeps the equation balanced.
Rewrite equation: Rewrite the equation by grouping the perfect square trinomial and combining the constants. $\newline$ $y = (x^2 - 4x + 4) - 4 - 1$ $\newline$ $y = (x - 2)^2 - 5$ $\newline$ We have now written the equation in vertex form, where $(x - 2)^2$ is the perfect square trinomial and $-5$ is the combination of the constants.