### Home > INT3 > Chapter 3 > Lesson 3.1.2 > Problem3-42

3-42.

If $p(x)=x^2+5x-6$: Homework Help ✎

1. Where does the graph of $y=p(x)$ intersect the $y$‑axis?

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

$(0,-6)$

2. Where does the graph of $y=p(x)$ intersect the $x$‑axis?

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

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

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

3. If $q(x)=x^2+5x$, what are the intercepts of the graph of $y=q(x)$?

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

$x$-intercepts: $(0,0)$, $(-5,0)$
$y$-intercept: $(0,0)$

4. Compare the graphs of $p(x)$ and $q(x)$.

The graph of $p(x)$ is $6$ units lower than the graph of $q(x)$.

5. What is $p(x)-q(x)$?

Subtract $q(x)$ from $p(x)$. How does your answer relate to part (d)?