If $p(x)=x^2+5x−6$, find:

1. Where $p(x)$ intersects the $y$-axis.

   Hint (a):

   Substitute $0$ for $x$, and solve for $p(x)$.

   Answer (a):

   $(0,-6)$

2. Where $p(x)$ intersects the $x$-axis.

   Hint (b):

   Substitute $0$ for $p(x)$, and solve for $x$.

   More Help (b):

   You can factor and use the Zero Product Property once you write your equation.

   Answer (b):

   $(-6,0)$ and $(1,0)$

3. If $q(x)=x^2+5x$, find the intercepts of $q(x)$ and compare the graphs of $p(x)$ and $q(x)$.

   Hint (c):

   Look at parts (a) and (b) to help find the intercepts.
   What do you notice about the graphs? Are they related?

   Answer (c):

   $x$-intercepts: $(0,0),(-5,0)$
   $y$-intercept: $(0,0)$
   $p(x)$ is $6$ units lower than $q(x)$.

4. Find $p(x)−q(x)$.

   Hint (d):

   Subtract $q(x)$ from $p(x)$. You should notice a relationship between your answers for parts (c) and (d).