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.
Answers
Reiny
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
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