SOLUTION: Find a quadratic model for each set of values 1. (-1,1) (1,1) (3,9)

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find a quadratic model for each set of values 1. (-1,1) (1,1) (3,9)      Log On


   

Question 1183874: Find a quadratic model for each set of values
1. (-1,1) (1,1) (3,9)
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find a quadratic model for each set of values
1.
(-1,1)
(1,1)
(3,9)

f%28x%29=ax%5E2%2Bbx%2Bc...........use point (-1,1)
1=a%28-1%29%5E2%2Bb%28-1%29%2Bc
1=a+-b+%2Bc.........solve for a
a=1%2Bb-c.........eq.1

f%28x%29=ax%5E2%2Bbx%2Bc...........use point (1,1)
1=a%281%29%5E2%2Bb%281%29%2Bc
1=a+%2Bb+%2Bc.........solve for a
a=1-b-c.........eq.2

f%28x%29=ax%5E2%2Bbx%2Bc...........use point (3,9)
9=a%283%29%5E2%2Bb%283%29%2Bc
9=9a+%2B3b+%2Bc.........solve for+a
9a=9-3b-c
a=1-b%2F3-c%2F9.........eq.3

from eq.1 and eq.2 we have
1%2Bb-c=1-b-c.........simplify
b=-b
2b=0
b=0
from eq.1 and eq.3
1%2Bb-c=1-b%2F3-c%2F9........substitute+b
1%2B0-c=1-0%2F3-c%2F9
1-c=1-c%2F9..........multiply by 9
9-9c=9-c
c-9c=9-9
-8c=0
c=0

then
a=1-0-0.........eq.2
a=1

since+a+=+1, b+=+0, c+=+0, your equation is f%28x%29=x%5E2+




Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The y value is 1 for both x=-1 and x=1; that means the line of symmetry is the y-axis. Then the equation is of the form y=ax^2+b.

Plug in the x and y values of any two of the given three points to get two equations in a and b and solve the pair of equations.

(1,1): 1 = a+b
(3,9): 9 = 9a+b

8 = 8a
a=1

1 = 1+b
b = 0

The quadratic equation is y = ax^2+b = 1x^2+1 = x^2

ANSWER: y=x^2