Question

identify the x-intercepts in the graph
y = 3x2 + 19x – 40.

Answer 1

Hint: Set y = 0

Answer 2

X intercepts are where the function crosses the x axis, where y = 0. Do you know how to solve the equation? \[3x^2+19x-40=0\]

Answer 3

Yeah , you factor out 3 next right?

Answer 4

You can only factor out 3 if the other two coefficients are common multiples of 3, which they are not.

Answer 5

Ok, so then what did you mean by set y=0? Could you explain that a little more?

Answer 6

@whpalmer4 already did it for you.

Answer 7

ooooh! ok Gotcha. ok so then what do I do after that? o.O

Answer 8

Factor the quadratic (if you know how)

Answer 9

As it doesn't look like factoring is going to get you anywhere, try the quadratic formula for the solution. If you have a polynomial \[ax^2+bx+c=0\] the solutions are \[x=-\frac{b\pm\sqrt{b^2-4ac}}{2a}\]

Answer 10

@whpalmer4, it's factorable

Answer 11

You may not have found all the possible factors. You assumed that because 19 is prime, there are no workable factors.

Answer 12

Wasn't saying it wasn't, just that if she didn't say "oh, got this" that she probably wasn't going to get anywhere

Answer 13

Ok, so if you can't factor out 3 OR 19 then do I factor 40?

Answer 14

i'm so lost -.-

Answer 15

Factoring the quadratic will require use of the 3, the 19, and the 40

Answer 16

Stumped?

Answer 17

yes -.-

Answer 18

Actually, we have to find two numbers that add to get 19, but multiply to get -120
a + b = 19
ab = -120

Answer 19

I'll just explain how I figured it out that way you can understand the reasoning.

Answer 20

So first I just thought of two numbers that might work.

First I tried 20 and -6 since 20 x -6 = -120. However, 20 - 6 = 14, so that doesn't work.

Then I tried 30 and -4. 30 x -4 = -120, but 30 - 4 = 26.

Now I know that the bigger number will be between 20 and 30. The only number that works is 24 and - 5 since 24 x -5 = -120 and 24 - 5 = 19

Answer 21

Now after doing this, I take the quadratic and "split the middle term" 19x so that
24x - 5x = 19x

Then I replace the expression appropriately in the quadratic:
3x^2 + 19x - 40 = 0
3x^2 + 24x - 5x - 40 = 0

Now from here, I place the first two terms and last two terms within a set of parentheses:
(3x^2 + 24x) + (-5x - 40) = 0

And afterwards, I factor the first two terms; then factor the last two terms to get:
3x(x + 8) - 5(x + 8) = 0

Now I see that x + 8 is also common to both terms so I factor that out as well to get:
(x + 8)(3x - 5) = 0

From here, you can use the zero product property to finish finding the x-intercepts.

Answer 22

so then you use FOIL to finish?

Answer 23

Zero Product Property is not the same as FOIL. If you FOILed, you would only get the quadratic back. That's the opposite of what we want to do. We are trying to solve for x which would tell us what the x-intercepts are.

Answer 24

ok so then I would do x+8=0 and 3x-5=0?
and solve them seperately?

Answer 25

Precisely

Answer 26

oooooh ok! so the answer is x=-8 and x=5/3

Answer 27

Bingo. So you found the x values. And now, you end by explicitly stating:
The x-intercepts are -8 and 5/3.

Any time you solve a word problem, you always end with a concluding statement.

Answer 28

Gotcha! thank you (: