Question

For a quadratic function, f(1)=5, f(2)=-7, f(3)=-11 find f(-2)

I'm studying for my exam and do not know how to do this. Please help me and tell me step by step. Thank you!

Answer 1

do you know the general form for a quadratic equation?

Answer 2

isn't it ax^2+bx+c

Answer 3

thats right. so you know your function is of the form:\[f(x)=ax^2+bx+c\]

Answer 4

a, b and c are three unknowns here

Answer 5

and you have been given three values for f(x)

Answer 6

you should be able to use these values to find a, b and c

Answer 7

so what i did was
a+b+c=5
4a+2b+c=-7
9a+3b+c=-11 but Im not sure what to do next to find f(-2)

Answer 8

use the 3 equations to solve for a, b and c.
then use these values of a, b and c to find f(-2)

Answer 9

does that make sense?

Answer 10

would a matrices help?

Answer 11

you could use matrices, but these equations are fairly simple. e.g.:
a+b+c=5 (1)
4a+2b+c=-7 (2)
9a+3b+c=-11 (3)

3a+b=-12 (2) - (1)
5a+b=-4 (3) - (2)

Answer 12

then eliminate b from the 2 new equations and solve for a
then find b
then find c

Answer 13

so i got f(-2)=-535…but i don't think that is right

Answer 14

i got a=4, b=-24, c=25

Answer 15

those are correct

Answer 16

so you now have:\[f(x)=4x^2-24x+25\]

Answer 17

how did you calculate f(-2)?

Answer 18

so i now got 89 i think i did something wrong on my calculator

Answer 19

yup - that's the correct answer - well done! :)

Answer 20

Thank you so much for your help!!

Answer 21

yw :)