Question

What is the average rate of change for this quadratic function for the interval from x=0 to x=2? A.3 B.4 C.6 D.2

Answer 1

Check the picture below.

so let's use those two points for that domain.

`\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x_1=0\\ x_2=2 \end{cases}\implies \cfrac{f(2)-f(0)}{2 - 0}\implies \cfrac{0~~ - ~~(-6)}{2}\implies \cfrac{6}{2}\implies 3`