The arrow diagram shows part of the function f(x)=ax^2 + bx + c which f(3)=32, f(1)=6 and f(-2)=-3. Find
a) the values of a, b and c,
b) the positive number x whose image is 2,
c) the set of numbers whose image under fis 2.

Hi, thank you for posting your question here at .

Area of Triangle = 1/2*base*height

For triangle ABC:

144 = 1/2*AC*(3x+x)
2(144) = AC(4x)
AC = 72/x

Through ratio and proportion:

(3x+x)/AC = x/DE
4x/(72/x) = x/DE
4x^2/72 = x/DE
4x/72 = 1/DE
DE = 72/4x = 18/x

For triangle DBE:

A = 1/2*base*height
A = 1/2*DE*x
A = 1/2*(18/x)*x
A = 1/2*18
A = 9 square units