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allsm [11]
3 years ago
6

Factor this expression completely and then place the factors in the proper location on the grid.

Mathematics
2 answers:
aalyn [17]3 years ago
5 0

For this case, we have to define the difference of squares:

a ^ 2-b ^ 2 = (a + b) (a-b)

We then have the following expression:

x ^ 2 - 9

From here, we observe that:

a = x\\b = 3

Therefore, replacing values we have:

x ^ 2 - 9 = (x + 3) (x-3)

Answer:

The factorization of the given expression is:

x ^ 2 - 9 = (x + 3) (x-3)

Sindrei [870]3 years ago
4 0
X^2 - 9 =
(x + 3)(x - 3)
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Answer:

y=-2\,(x-6)^2+246

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This agrees with the last option in the list of possible answers

Step-by-step explanation:

Recall that the maximum of a parabola resides at its vertex. So let's find the x and y position of that vertex, by using first the fact that the x value of the vertex of a parabola of general form:

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In our case, the quadratic expression that generates the parabola is:

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This is the price of the video game that produces the maximum profit (x = $6). Now let's find the y-position of the vertex using the actual equation for this value of x:

y=-2x^2+24x+174\\y_{vertex}=-2\,(6)^2+24\,(6)+174\\y_{vertex}=-72+144+174\\y_{vertex}=246

This value is the highest weekly profit (y = $246).

Now, recall that we can write the equation of the parabola in what is called "vertex form" using the actual values of the vertex position (x_{vertex},y_{vertex}):

y-y_{vertex}=a\,(x-x_{vertex})^2\\y-246=-2\,(x-6)^2\\y=-2\,(x-6)^2+246

Therefore the answer is:

y=-2\,(x-6)^2+246

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