Question 1208053
<pre>
For h(x) = -2x^2 + x, 

A. Find the average rate of change from 0 to .<pre>As x goes from 0 to 3, y [or h(x)] goes from h(0)=-2(0)^2 + 0=0 to h(3)=-2(3)^2 + (3)=-15

From 0 to -15 is a change of (-15)-(0)=-15 in y

From 0 to 3 is a change of (3)-(0) = +3 in x

So the average change in y [or h(x)] per the +3 average change in x
is -15 units change in y per a +3 change in x, which means an average
change of (-15)/(+3)=-5 y-units change per x-units change.

That's what the slope is, the change in y, divided by the change in x 

Answer: -5 change in h(x) y-units per x-unit change.</pre>B. Find an equation of the secant line containing (0, h(0)) and (3, h(3)).<pre>
{{{m}}}{{{""=""}}}{{{matrix(1,3,change,in,y)/matrix(1,3,change,in,x)}}}{{{""=""}}}{{{(-15)/(""+3)}}}{{{""=""}}}{{{-5}}}

{{{y-y[1]}}}{{{""=""}}}{{{m(x-x[1])}}}

{{{y-(0)}}}{{{""=""}}}{{{-5(x-(0))}}}

{{{y}}}{{{""=""}}}{{{-5x}}}

change y to h(x)

{{{"h(x)"}}}{{{""=""}}}{{{-5x}}}

{{{drawing(400,400,-1,4,-17,1,line(-3,15,5,-25), locate(0,0,"(0,0)"),
locate(3,-15,"(3,-15)"),
graph(400,400,-1,4,-17,1,-2x^2 + x))}}}

The black line is the secant line. It has two points
in common with the function h(x) (the red curve).

Remember what the word "secant" means, a line that cuts
through a curve, as you can see, the black line cuts through
the red curve, which is the graph of y = h(x). 

[Remember from your geometry that a secant line was a line
that cuts through a circle.] 

Edwin</pre>