Question

Please help

You are given the coordinates of the vertex (8,8) and of a point (5,1) on a parabola. Find the coefficients for the equation of the parabola.

Answer 1

do you know the vertex form?

Answer 2

No I dont

Answer 3

y = a(x-h)^2 + k, where (h,k) is the vertex and a is non-zero constant.

What is (h,k) in this case?

Answer 4

(8,8)

Answer 5

if you plug that in the formula, what do you get?

Answer 6

y=a(x-8)^2+8

Answer 7

@sourwing I'm not sure what to do from here

Answer 8

they tell you point (5,1) is on the curve.
replace x with 5, and y with 1
and solve for a

Answer 9

now you need to find a. Which is why another point is given (x,y) = (5,1)

Answer 10

Alright thank you both but I need to Find the coefficients for the equation of the parabola

I just have to answer like this y = x2 + x + . Basicly fill in the blanks

Answer 11

First, are you able to find a using
1 = a(3-8)^2 +8
?

Answer 12

yes Im @phi

Answer 13

-7/9

Answer 14

ok, that means your equation is
\[ y = -\frac{7}{9}(x-8)^2 +8 \]
to put this in standard form, expand (x-8)^2
then distribute the -7/9

Answer 15

@phi Im not sure on how to expand this

Answer 16

(x-8)(x-8)
do you know FOIL? First, outer , inner , last?

Answer 17

or use the distributive law
if it were A*(x-8) you would do Ax - A*8
now if A was (x-8) this means Ax - A8= (x-8)x - (x-8)*8
now distribute again.

Answer 18

see
http://www.khanacademy.org/math/algebra/multiplying-factoring-expression/multiplying-binomials/v/multiplying-binomials

Answer 19

alright thank you

Answer 20

OR - and this is a REALLY BIG "or" \((y-8)^{2} = -\dfrac{49}{3}(x-8)\)

There just isn't enough information to determine if Vertical or Horizontal orientation is intended. There are TWO solutions with Axis of Symmetry parallel to a coordinate axis.

Answer 21

@tkhunny I just have to answer like this y = x2 + x + . Basicly fill in the blanks

Answer 22

You didn't SAY that. That information rules out the Horizontal Axis of Symmetry. If you don't say it, you didn't say it. Wow! Can I copyright that?

Answer 23

if you multiply out \( (x -8)^2 \) you should get
\[ (x -8)^2 =(x-8)(x-8)\\=x^2 -8x -8x +64\\= x^2-16x +64\]

that means your equation
\[ y = -\frac{7}{9}(x-8)^2 +8 \\y= -\frac{7}{9}\left(x^2-16x +64\right)+8 \]
now distribute the -7/9 (which means multiply each term inside the parens by -7/9 and then drop the parens)