SOLUTION: Here I have a question which is part of a homework assignment, I solved a and b but got lost at c. Any help would be greatly appreciated! https://drive.google.com/file/d/1gVccbV

Algebra ->  Graphs -> SOLUTION: Here I have a question which is part of a homework assignment, I solved a and b but got lost at c. Any help would be greatly appreciated! https://drive.google.com/file/d/1gVccbV      Log On


   

Question 1189167: Here I have a question which is part of a homework assignment, I solved a and b but got lost at c. Any help would be greatly appreciated!
https://drive.google.com/file/d/1gVccbVm6nXG5QGGxJJfnzC--ZO4QUK5o/view?usp=sharing
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

c.
y=ax%5E2%2Bbx%2Bc
use three given points on parabola to calculate a, b, and c
(0,2)
(0.4,8)
(3,2)

y=ax%5E2%2Bbx%2Bc......if (0,2)
2=a%2A0%5E2%2Bb%2A0%2Bc
c=2.......................eq.1

y=ax%5E2%2Bbx%2Bc......if (0.4,8)
8=a%2A0.4%5E2%2Bb%2A0.4%2Bc...........substitute c
8=0.16a+%2B+0.4+b%2B2..............solve for b
8-0.16a+-2=+0.4+b
6-0.16a+=+0.4+b
b=%286-0.16a%29%2F0.4
b=15+-+0.4a............eq.2


y=ax%5E2%2Bbx%2Bc......if (3,2).......substitute b and c
2=a%2A3%5E2%2B%2815-+0.4a%29%2A3%2B2.........solve for+a
2=7.8+a+%2B+47
7.8+a=2-+47
+a=-+45%2F7.8
a=-75%2F13

go to eq.2, substitute a

b=15+-+0.4%28-75%2F13%29............eq.2
b=225%2F13

so, your equation is y=-%2875%2F13%29x%5E2%2B%28225%2F13%29x%2B2