Question

What are the x-intercepts of the graph of y=12x^2-5x-2?

A) 1 and -1/6
B) -1 and 1/6
C) 2/3 and -1/4
D) -2/3 and 1/4

Answer 1

the x-intercept is when y=0. so basically you will want to factor the right side and find it's two zeroes.

Answer 2

so quadratic formula?

Answer 3

i mean completing the square

Answer 4

please help

Answer 5

quadratic formula will work.

Answer 6

i completed the square... but im confused where to go from there

Answer 7

Can you show what you've got for completing square?

Answer 8

I got down to this
y+2= (x-5/2)^2

Answer 9

how dow i find the x-ints.?

Answer 10

That doesn't look right. How did you get it?

Answer 11

To find x intercepts, you put y=0 and solve for x.

Answer 12

y+2=1(12x^2-5x+25/4)
y+2=(x-5/2)^2

Answer 13

how do I find two x-ints? one I plug in 0 but then the other?

Answer 14

1. That's not the right way to do completing square.
2. You can find two x-ints by putting y=0 into the equation, since the degree of y is 2 and delta is not 0. You need to solve x.

Answer 15

To do completing square, you need to factorize the first two term and pick the coefficient of x^2 as the common factor, that is 12 in this case.
\[y=12x^2-5x-2\]\[y=12(x^2-\frac{5}{12}x)-2\]Then, you need to add and subtract the same term inside the bracket. What would it be?

Answer 16

so I did the quadratic formula instead and got (5plus or minus 11)/24

Answer 17

Looks good.
So, the first x would be (5+11)/24, and the second x would be (5-11)/24

Answer 18

isn't that answer what y equals?

Answer 19

No, that's what x equals to. Since you've put y=0 to solve x.

Answer 20

wait.. isn't it a y equals equation?
kinda confused

Answer 21

y=12x^2-5x-2
To find x-ints, put y=0. So,
0=12x^2-5x-2
Using quadratic formula,
\[x= \frac{-(-5)\pm \sqrt{(-5)^2 - 4(12)(-2)}}{2(12)}\]
It's the x which you're solving using the quadratic formula.

Answer 22

so the x-ints would be -1/4 and 2/3 right

Answer 23

Yes.

Answer 24

A plot is attached.