Question

What are the x-intercepts of the graph of f(x)?

f(x) = 2x^2 − x − 10


*I have to solve for it and not use desmos* ._.

Answer 1

Plug and chug
(2x +/- _ )(x +/- _)
You know that we have factors of 1, 10 or 2, 5
Obviously it can't be 1, 10, or else no matter what order we put it in, we won't get -x

So 2 and 5, which one's positive, which one's negative, which one gets multiplied with x, which one gets multiplied with 2x?

Answer 2

:( im confused-

Answer 3

By the way, a hint 2x times 2 is 4x, while 5x alone is 5x, adn 4x - 5x is -x
So whichone is negative, which one is positive
which one is multiplied by 2

Answer 4

...

Answer 5

(2x +/- __)(x +/- __)
you do get how that is made, right?

Answer 6

uh- is it factoring

Answer 7

2x times x is 2x^2, that's why we have 2x and x

Answer 8

ah ok, I understand

Answer 9

Okay so now try them all in, you know for sure we use 2 and 5, right?

Answer 10

yea? bc 2 x 5 = 10

Answer 11

Yes so then it's
(2x +/- 2or5)(x +/- 2or5)

Answer 12

Since I have no idea how to coherently explain this to you again, i suggest trying each of them
-2, 5
2, -5
-5, 2
-2, 5 o-O

Answer 13

want me to try explaining?

Answer 14

yes angle explain o-o

Answer 15

if you have been taught the FOIL method before, this is just that idea but backward
> yes it is factoring

Answer 16

you are looking for two numbers that:
multiply to get -20 [because the first 2 and the last -10 multiplied is -20]
and
add up to -1 [because the middle coefficient is -1 times the middle x]

Answer 17

I will rephrase:
two numbers that multiply to get -20 but also add up to -1

Answer 18

usually people use "guess and check" to get their numbers
1, 20
2, 10
4, 5
all multiply to get 20

but only 4 - 5 = -1

this means we want to use 4 and -5 as our numbers

Answer 19

ah ok, I understand

Answer 20

awesome

now, what I am going to do next is called factoring by grouping

It uses the idea that
4x - 5x = -x
which means we can go the other way and split up the -x in the middle

-x = 4x - 5x
means

2x^2 - x - 10
turns into
2x^2 + 4x - 5x - 10

Answer 21

If I have
2x^2 + 4x - 5x - 10

this can also look like
(2x^2 + 4x) + (-5x + -10)

can you try factoring out the greatest common factor out of each pair?

Answer 22

uh.. 2x(x+2) and -5(x+2)

Answer 23

amazing!

Answer 24

then notice how they have (x+2) in common

you can factor that to the front as well

Answer 25

:0 I thought I was wrong- ty

Answer 26

so would it be...

(x+2)(2x-5)

Answer 27

awesome!

(x+2)(2x-5) = 0

do you know how to solve for x in this?

Answer 28

umm, I dont think so 0-0

Answer 29

you take each of the stuffs in the parenthesis and set it equal to 0

x+2 = 0

and

2x - 5 = 0

after solving for x, those would be your answer(s)

Answer 30

ah yes, it would be -2 and 2.5

Answer 31

those should be your answers :)

what we did was:
Step 1: we factored the expression by looking for the two numbers that multiply to the first and third coefficients and added to the middle coefficient
Step 2: we split the middle value into the two numbers we found in step 1
Step 3: we factored the two chunks
Step 4: we factored the things they had in common
Step 5: we set each chunk equal to zero and solved

Answer 32

these steps will always work for finding the x-intercept

Answer 33

*of a parabola

Answer 34

Thank you so much :)