Question

For a particular quadratic function f(x)=ax^2+bx+c, f(−3)=−13 and f(2)=7. If a=−3, find b and c.

Answer 1

just plug in ....
f(-2) = -13
4a - 2b + c = -13

f(2) = 7
4a + 2b + c = 7

but a = -3, so
-12 - 2b + c = -13
-2b + c = -1 ****

-12+2b+c = 7
2b + c = 19 ***

add the equation marked ***
2c = 18
c = 9
in 2b+c=19
2b+9=19
b = 10
b = 5

a = -3, b=5, c=9