Question

What is the slope of the line through (-1,-2) and (x,y) for y = x2 + 2x + 1 and x=-0.90?  x=-1.05?  x=h-1? What happens to this last slope when h is very small? Round-off your answers to 2 decimal places whenever possible.  Use the ^ symbol to express the exponent of a variable, i.e. x^2 (x squared). Do not use spaces on your answers

Answers:

when x=-0.90: m = _____________

when x=-1.05: m = ____________

when x=h-1: m = ___________ /h

when h approaches 0: m = _______________

Answer 1

A point P has the coordinates (x,x^2+2x+1). The quadratic can be expressed as (x+1)^2.

Slope=m=∆y/∆x=(x^2+2x+1+2)/(x+1)=(x^2+2x+3)/(x+1).

When x=-0.90, m=20.1

When x=-1.05, m=-40.05

When x=h-1, m=(h^2-2h+1+2h-2+3)/h=(h^2+2)/h.

When h→0, m→h+2/h=∞ (infinity) The angle of slope approaches 90 degrees (vertical).