jmc

Question

A portion of the graph of f(x)=ax^2+bx+c is shown below. The distance between grid lines on the graph is 1 unit. What is the value of a+b+2c? FIGURE

Accepted Answer

Note that align* f(0) &= a(0)^2+b(0)+c &=c align*and align* f(1) &= a(1)^2+b(1)+c &=a+b+c. align*Thus, align* a+b+2c &= c + (a+b+c) &= f(0)+f(1). align*The graph of y=f(x) passes through (0,7) and (1,4), so f(0)=7 and f(1)=4. Therefore, a+b+2c = 7 + 4 = 11.