- For the equation $y = x^2 + 3 $ :
- Find the average slope between $x = 2 $ and $ x = 4$
- Find the average slope between $x = -4 $ and $ x = -2$
- Find the average slope between $x = -2 $ and $ x = 2$
- Determine what value of x will give a slope of zero.
Solution:
- $\frac{4^2 + 3 - (2^2 + 3)}{4 - 2} = 6 $
- $\frac{(-2)^2 + 3 - ((-4)^2 + 3)}{-2 - -4} = -6 $
- $\frac{2^2 + 3 - ((-2)^2 + 3)}{2 - -2} = 0 $
- When $x = 0$, the slope is zero