Question

I really need help with these!


You must show your work on each of the following questions.

1. In the following equation, identify the x-intercepts in the graph y = 3x^2 + 19x – 40.

2. The dimensions of Eric’s pool are 9 feet by 7 feet. He wants to build a walkway surrounding the pool so that the square footage of the walkway and pool is 143 square feet. How wide is one side of the walkway? Use the picture below to help you. (I put the image below)

Answer 1

But it says to find the x intercepts

Answer 2

The x axis is defined as being the line in a coordinate system where y=0. So to find the x intercepts, plug in 0 for y and solve for x:

Answer 3

0=3x2+19x−40

Answer 4

Factor the quadratic
0=(x+8)(3x−5)

Answer 5

Looking at this equation now, there are only two ways it can be true: either the first parentheses group is 0 or the second parentheses group is 0. So now solve each for 0.

Answer 6

0=x+8
x=−8
And the 2nd one:
0=3x−5
3x=5
x=53

Answer 7

So the two possible values for x that will make y=0 are x=-8 and x=5/3, and these are also where the graph intercepts the x axis.

Answer 8

ohh okay thank you! @some_someone

Answer 9

what about the second one? @some_someone