Question

Write the equation (in vertex form) for the parabola with the given vertex and passing through
the given point.
Vertex (2,0) point (1,4)

Answer 1

a parabola will have the same form as a the standard form used in the last question, like this:

Ax^2 + Bx + C = 0

Answer 2

alrighty but which numbers do you use for what?

Answer 3

one second, i'm finding it so i teach you right..

Answer 4

alright

Answer 5

ok ok, for get what I said before..

so it's like this:
the vertex has the terms (h, k)
so we have (2,0)
so that means
h = 2
k= 0

make sense?

Answer 6

yupp

Answer 7

now here is the form for the parabola:
y = a(x-h)^2 + k
we know what h and k are,
and the point given to us of (1,4) we can use for x and y,
so we will need to plug those numbers in and solve for a

Answer 8

soo hmm (1-2)^2+0??

Answer 9

dont forget the part "y = a(" and plug in y, becuase we know what that is

Answer 10

never mind it says just write the equation..

Answer 11

right, but we arn't done, we have to find what a is equal to to wrtie the equation

Answer 12

o alright, soo hmm 4=a(1-2)^2+0

Answer 13

good good,
now solve for a

Answer 14

is it 4?.....4=4(1-2)^2+0

Answer 15

i'll walk you through it-

Answer 16

4=a(1-2)^2+0
4=a(-1)^2
4=a(1)
a=4, then we put it into the proper form, plug in h, k, a, but not x and y into this equation:
y = a(x-h)^2 + k

Answer 17

umm 4(x-2)^2+0

Answer 18

very good, just don't forget the y=, so like this:
y=4(x-2)^2

good job

Answer 19

so what the equation means is that we can plug in any x value we want, and it will spit out the value of Y for that parabola

good job

i have to go for the night

Answer 20

alright thanks alot