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Complete the square to re-write the quadratic function in vertex form:

y=x^(2)+3x-6
Answer:
y=

Complete the square to re-write the quadratic function in vertex form: $\newline$ $y=x^{2}+3 x-6$ $\newline$ Answer: $y=$

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Write a quadratic function in vertex form

Full solution

Q. Complete the square to re-write the quadratic function in vertex form:

\newline

y=x^{2}+3 x-6

\newline

Answer:

y=

Identify vertex form: Identify the vertex form of a parabola. $\newline$ The vertex form of a parabola is $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Begin with function: Begin with the given quadratic function. $\newline$ We have $y = x^2 + 3x - 6$ .
Prepare for completion: Prepare to complete the square. $\newline$ To complete the square, we need to form a perfect square trinomial from the $x^2$ and $x$ terms. We will add and subtract the square of half the coefficient of $x$ inside the parentheses. $\newline$ The coefficient of $x$ is $3$ , so half of $3$ is $\frac{3}{2}$ , and the square of $\frac{3}{2}$ is $(\frac{3}{2})^2 = \frac{9}{4}$ .
Add/subtract $\frac{3}{2}$ ^ $2$ : Add and subtract $\frac{3}{2}$ ^ $2$ inside the equation. $y = x^2 + 3x + \left(\frac{9}{4}\right) - \left(\frac{9}{4}\right) - 6$ Now we have added and subtracted $\frac{9}{4}$ to complete the square.
Rewrite equation: Rewrite the equation grouping the perfect square trinomial and combining the constants. $\newline$ $y = (x^2 + 3x + \frac{9}{4}) - \frac{9}{4} - 6$ $\newline$ $y = (x + \frac{3}{2})^2 - \frac{9}{4} - \frac{24}{4}$ $\newline$ $y = (x + \frac{3}{2})^2 - \frac{33}{4}$ $\newline$ Now we have the equation in vertex form.

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