Question

(0,8),(2,10),(3,2) find a quadratic function that includes the set of values below

Answer 1

`-3x^2+7x+8`

Explanation:

The standard form for a quadratic is ax^2+bx+c

First plug in (0,8).

8=a(0)^2+b(0)+c

c=8

Then, plug in the other two

a(2)^2+(2)b+c=10

4a+2b+c=10

a(3)^2+(3)b+c=2

9a+3b+c=2

Since we know that c=8, let's also plug that in.

4a+2b+8=10

4a+2b=2

9a+3b+c=2

9a+3b=-6

Then, make the b's equal

3(4a+2b=2)

12a+6b=6

2(9a+3b=-6)

18a+6b=-12

Then subtract

18a+6b=-12

-(12a+6b=6)

6a=-18

a=-3

Plug in a=-3

18(-3)+6b=-12

-54+6b=-12

6b=42

b=7

Double check

Application: Desmos