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

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) (Show Source): You can put this solution on YOUR website!

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

...........use point (,)

.........solve for
.........eq.1

...........use point (,)

.........solve for
.........eq.2

...........use point (,)

.........solve for

.........eq.3

from eq.1 and eq.2 we have
.........simplify

from eq.1 and eq.3
........substitute

..........multiply by

then
.........eq.2

since, , , your equation is

Answer by greenestamps(13200) (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

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