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2-17.

If $p(x)=x^2+5x−6$, find: Homework Help ✎

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

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

$(0,-6)$

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

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

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

4. Find $p(x)−q(x)$.

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