Question

Graph the solution to the following inequality on the number line.
(x+2)(x-7)>0

Answer 1

(x + 2)(x - 7) >0
x^2 - 5x - 14 > 0

Graph x^2 - 5x - 14

Answer 2

Then observe the areas above the x axis where the graph is true.

Answer 3

Okay, how did you get rid of the parenthesis?

Answer 4

I multiplied it out. You know how to multiply polynomials, right?

Answer 5

(x + 2)(x - 7) = x(x - 7) + 2(x - 7) = x^2 - 7x + 2x - 14 = x^2 - 5x - 14

Answer 6

Ohh, right right.

Answer 7

(x + 2)(x - 7)
= x(x - 7) + 2(x - 7)
= x^2 - 7x + 2x - 14
= x^2 - 5x - 14

Answer 8

Do you know what the solution is now?

Answer 9

I'd forgotten about that. So how do I get x^2 - 5x - 14 onto a number line?
Just starting school again and am still getting into the swing of things.

Answer 10

It makes sense for a graph, but number line?

Answer 11

I will try to explain it to you.

Answer 12

Do you at least remember how to find the zeroes of the quadratic expression?

Answer 13

Yes

Answer 14

What are the zeroes?

Answer 15

Okay. I guess I'll just explain

Answer 16

To get the zeros wouldn't we have to take it back to binomials?

Answer 17

The zeroes of the graph are

x = -2 , x = 7

Because

x^2 -5x - 14 factors to (x + 2)(x - 7) and using the zero product property

x + 2 = 0
x = -2

x - 7 = 0
x = 7

Answer 18

We graph that on the number line.

Answer 19

Got it! I guess I was just overthinking the problem

Answer 20

We're not done yet...

Answer 21

Trust me..there's more

Answer 22

Allow me to finish completely

Answer 23

Okay

Answer 24

Next we find the vertex of the parabola since a quadratic expression is graphed as a parabola...

We use the vertex of a parabola formula to find the vertex:

\[x = -\frac{b}{2a}\]

a = 1
b = -5


\[x = \frac{5}{2} = 2 \frac{1}{2}\]

Answer 25

then we have to insert that into x to find y:

We need to graph the quadratic expression:

After inputting x and solving for y we get:

y = (5/2)^2 -5(5/2) - 14 = -41/4 or -10 1/4