Question

Use the graph below for this question: graph of parabola going through negative 1, 5 and negative 2, 7.

What is the average rate of change from x = −1 to x = −2?
a:2
b:-2
c:4
d:-1

Answer 1

Let the function be
`f(x)=ax^2+bx+c`. (this is the general form of a quadratic equation, whose graph is a parabola. a is different from 0)

The average rate of change from x=-1 to x=-2 is found by the formula:


`(f(-2)-f(-1))/((-2)-(-1))= (f(-2)-f(-1))/((-2)+1)= (f(-2)-f(-1))/(-1)=-f(-2)+f(-1)`.

We are given the points (-1, 5) and (-2, 7), so we have f(-1)=5 and f(-2)=7, thus

-f(-2)+f(-1)=-7+5=-2.


Answer: b: -2