### Home > A2C > Chapter 4 > Lesson 4.1.3 > Problem4-43

4-43.

Make predictions about how many places the graph of each equation below will touch the $x$-axis. You may first want to rewrite some of the equations in a more useful form.

1. $y = \left(x − 2\right)\left(x − 3\right)$

How many x-intercepts will this equation have?

1. $y = \left(x + 1\right)^{2}$

See part (a).

1. $y = x^{2} + 6x + 9$

Factor the right side in order to find the intercepts.

1. $y = x^{2} + 7x +10$

Look at parts (a) through (c). Remember to factor first to find the x-intercepts.

1. $y = x^{2} + 6x + 8$

Look at parts (a) through (d).

1. $y = −x^{2} − 4x − 4$

Look at parts (a) through (d). Remember to factor $−1$ out.