Question

find the x-intercept of a parabola with vertex (-1,2) and y-intercept (0,-3) formula (y-k)=a(x-h)

Answer 1

@terenzreignz

Answer 2

Well, the vertex of the parabola would be (h, k)

Answer 3

So you can replace the h by -1
and the k by 2

Answer 4

so -1-2=a(0-(-3)^2

Answer 5

Yes, and solve for a.

Answer 6

That doesn't end things yet, though, but do solve for a...

Answer 7

WAIT

Answer 8

Why did you replace y with -1?

Answer 9

Let's start from the beginning...

Answer 10

lol my bad

Answer 11

\[\large (y-k) = a(x-h)^2\]
Where (-1, 2) is the vertex, right?

Answer 12

yes

Answer 13

So, in general,
In the equation\[\large (y-k) = a(x-h)^2\]
The vertex is at the point (h, k)
So you can replace (h,k) with (-1 , 2)
And what do you get?

Answer 14

0-(-1)=a(-3-2)^2

Answer 15

Okay... that's the next step ahead.... now solve for a.

Answer 16

1=a(25) im stuck here would i divide by 25?

Answer 17

Yup. Don't worry about fractions....

Answer 18

so a=1?

Answer 19

No... if you divide both sides by 25, you get
\[\large a =\frac1{25}\]

Answer 20

so a is 1/25

Answer 21

So, now you have your equation
\[\huge y - 2 = \frac1{25}(x +2)^2\]

Answer 22

Wait a sec... I seem to have gotten another mix-up

Answer 23

Let's start from the beginning... again
\[\large (y-k) = a(x-h)^2\]

Answer 24

the answer has to be to the nearest tenth

Answer 25

And don't skip steps... please :)
for now, replace (h , k) with (-1 , 2)

Answer 26

\[y-2=a(x-(-1)^2\]

Answer 27

You got it backwards earlier
\[\large y - 2 = a(x - (-1))^2\]

Answer 28

Now, put in the y intercept, and replace
(x , y) with (0 , -3)

Answer 29

\[-3-2=a(0-(-1))\]

Answer 30

Okay, don't forget the squared at the end...
NOW solve for a.

Answer 31

a=-5

Answer 32

Yup...
So now we have...
\[\large y - 2= -5(x + 1)^2\]
To get the x-intercepts, set y = 0, and solve for x.

Answer 33

idk how to do that lol

Answer 34

Set y = 0
\[\huge 0 - 2 = -5(x+1)^2\]

Answer 35

\[\Large -2 = -5(x+1)^2\]

Answer 36

Maybe you ought to try a bit harder... I'll be off for a bit, I'll be back in a few minutes..

Answer 37

x=1

Answer 38

@Mertsj maybe instead of expanding, you can divide both sides by -5 and just take the square roots?

Answer 39

umm okay??

Answer 40

Yeah... what that guy said ^
LOL
divide both sides by -5
\[\huge \frac{-2}{-5}=(x+1)^2\]

Answer 41

so, simplifies to...
\[\large \frac25=(x+1)^2\]

Answer 42

Taking the square roots of both sides gives you...
\[\large \sqrt{\frac25}=x+1\]

Answer 43

sorry
\[\large \pm\sqrt{\frac25}=x+1\]

Answer 44

And now, you can solve for x, quite simply :)

Answer 45

.3675

Answer 46

Don't forget the plus or minus...

Answer 47

im so confused now

Answer 48

Okay..., so solving for x gives us...
\[x = -1 \pm \sqrt{\frac25}\] right?

Answer 49

yes

Answer 50

So, take both \[-1+\sqrt{\frac45}\]and\[-1-\sqrt{\frac45}\]

Answer 51

And those are your x-intercepts.

Answer 52

so (-5,0) (1,0)

Answer 53

the answer has to be put like this (x1,y1) (x2,y2) to the nearest hundred

Answer 54

??

Answer 55

Yeah... the x intercepts look like these...
(x1 , 0) and (x2 , 0 )
since the y-values on x-intercepts are always zero.