### Home > CCA2 > Chapter 2 > Lesson 2.1.3 > Problem2-39

2-39.

Make predictions about how many times 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. Homework Help ✎

1. $y=(x−2)(x−3)$

How many $x$-intercepts are there?

$2$

1. $y=(x+1)^2$

$1$

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

$1$

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.

1. Check your predictions with your calculator.

2. Write a clear explanation describing how you can tell whether the graph of a parabola will touch the $x$-axis at only one point.

What pattern did you notice above?