### Home > A2C > Chapter 4 > Lesson 4.1.2 > Problem4-19

4-19.

If $p\left(x\right) = x^{2} + 5x − 6$, find:

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

Set $x$ to $0: p\left(x\right) = \left(0\right)^{2} + 5\left(0\right) − 6$

$p\left(x\right)$ intersects the y-axis at $\left(0, −6\right)$.

1. Where $p\left(x\right)$ intersects the x-axis.

Set y to $0: \left(0\right) = x^{2} + 5x − 6$

$0 = \left(x + 6\right)\left(x − 1\right)$

$p\left(x\right)$ intersects the x-axis at $\left(−6, 0\right)$ and $\left(1, 0\right)$.

1. If $q\left(x\right) = x^{2} + 5x$.

1. Find the intercepts of $q\left(x\right)$ and compare the graphs of $p\left(x\right)$ and $q\left(x\right)$.

2. Find $p\left(x\right) − q\left(x\right)$.

Follow the steps in parts (a) and (b).

How are the positions of the graphs different? Are their sizes different?

Subtract the two expressions.