Question

HELP! MEDAL?
find the x-intercept of the parabola with vertex (1,1) and y intercept (0,-3) write your answer in this form: (x1,y1),(x2,y2) if necessary round to the nearest hundredth

Answer 1

you can find the equation of the parabola
then find the x-intercepts

Answer 2

\[y=a(x-h)^2+k \]
you are given (h,k) already plug that in
you can solve for a by using the other point

then to find the x-intercepts you set y to 0 and solve for x

Answer 3

@Love.Kat123 let me know if you have any questions

Answer 4

im confused by it all math isnt my strong suit

Answer 5

do you know what h and k are?

Answer 6

(h,k) is the vertex
you are given h=? and k=?

Answer 7

you are given the vertex is (1,1)
(1,1)=(h,k)
so h=? and k=?

Answer 8

1?

Answer 9

both are 1 yes
so plug those in
\[y=a(x-h)^2+k \\ y=a(x-1)^2+1\]

Answer 10

now find a using the other point

Answer 11

(x,y)=(0,-3)
so replace x with 0 and y with -3
and solve for a

Answer 12

ugh im so confused and frustrated i have no idea what your talking about im legit going to cry

Answer 13

you should see see an x and y in my equation above

Answer 14

I'm asking you to replace x with 0 and y with -3

Answer 15

then solve for a

Answer 16

please show me as far as you can get with my last instruction

Answer 17

i can get about as far as reading the question
i should have taken those classes more seriously

Answer 18

\[\color{red}y=\color{green}a(\color{blue}x-1)^2+1\]
do you see the x and the y there?
we are trying to use x=0 and y=-3 to find a

Answer 19

like can you at least replace the x with 0 and the y with -3?

Answer 20

like that is all I'm asking you to do right now
just one step ... replacing x with 0 and y with -3

Answer 21

yes... maybe ... i think

Answer 22

can you show me what you have please

Answer 23

wait is x1 0 and y1 -3

Answer 24

though that is a y-intercept not an x-intercept

Answer 25

Can you please replace the x in my equation with 0
and replace the y in my equation with -3

Answer 26

\[\color{red}y=\color{green}a(\color{blue}x-1)^2+1 \]
the y is in red
the x is in blue

Answer 27

replace that blue letter with 0
replace that red letter with -3

Answer 28

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

Answer 29

great so notice you have enough information to solve for a

Answer 30

wait is that right

Answer 31

it doesnt say anything about a

Answer 32

oh my im going to fail D:

Answer 33

yes it does...
you even typed a...
see the a in
-3=a(0-1)^2+1

Answer 34

first let's do the operation next to a
(0-1)^2=?

Answer 35

uh.... what

Answer 36

if you take 1 away from 0 you have -1...
(-1)^2=?

Answer 37

i think im going to have a panic attack

Answer 38

you are going to have a panic attack over me asking you to evaluate (-1)^2?
why?

Answer 39

(-1)^2 is the same as saying -1 times -1

Answer 40

I know you can do that

Answer 41

but the just equals -1 :|

Answer 42

-1 times -1 isn't -1
\[-3=a(0-1)^2+1 \\ -3=a(-1)^2+1 \\ \\ -3=a(1)+1 \\ -3=a+1\]

Answer 43

-1 times -1 is 1

Answer 44

anyways solve -3=a+1 for a

Answer 45

okay um a=-2

Answer 46

how did you get -2?

Answer 47

subtract 1 on both sides gives
-3-1=a+1-1
or
-3-1=a

Answer 48

-3-1 is?

Answer 49

you said -3=a+1
-3+1=-2

Answer 50

-3-1=-4

Answer 51

you cannot solve for a that way

Answer 52

you cannot subtract 1 on one side and do the oppsite to the other other side

Answer 53

-3=a+1
gives us a=-3-1 not -3+1

Answer 54

anyways yet a=- 4
since -4+1 is -3

Answer 55

\[y=a(x-h)^2+k \text{ is vertex form for a parabola } \\ (h,k)=(1,1) \\ y=a(x-1)^2+1 \\ \text{ we used} (0,-3) \text{ to find } a \\ \\ a=-4 \\ y=-4(x-1)^2+1 \\ \text{ we now have everything we need to find the } x-\text{intercepts }\]

Answer 56

so to finally find the x-intercepts we set y to 0 and solve for x

Answer 57

x-intercepts lay on the x-axis
this is why y is 0 there

Answer 58

so you already have the y-coordinates for both your answers
we are looking for the x-coordinates

Answer 59

and again to find those replace y with 0 and solve for x

Answer 60

whats a x-axis

Answer 61

the horizontal axis that is also know as the line y=0