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3 years ago

Write the vertex form of y = -x^2 + 6x + 6.

Mathematics

1 answer:

user100 [1]3 years ago

4 0

Answer:

y = - (x - 3)² + 15

Step-by-step explanation:

using the method of completing the square

y = x² + 6x + 6 ← factor out - 1 from the first 2 terms

y = - (x² - 6x) + 6

to complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 6x

y = - (x² + 2(- 3)x + 9 - 9) + 6

= - (x - 3)² + 9 + 6

= - (x - 3)² + 15

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In the first column, we have x = -4 and y = 3.5. Substituting these values for x and y, we have

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In the second column, x = -2 and y = 7.

Now lets substitute the value of x for -2. If we get y to be 7, then the relationship is an inverse variation

We have

$\begin{gathered} y=\frac{-14}{x} \\ y=\frac{-14}{-2} \\ y=7 \end{gathered}$

Since we got y = 7, the relationship is therefore an inverse variation.

The constant k = -14

The equation for the inverse variation is

$y=\frac{-14}{x}$

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