CPM Homework Help : A2C Problem 4-43

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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.

$y = \left(x − 2\right)\left(x − 3\right)$
Hint (a):
How many x-intercepts will this equation have?

$y = \left(x + 1\right)^{2}$
Hint (b):
See part (a).

$y = x^{2} + 6x + 9$
Hint (c):
Factor the right side in order to find the intercepts.

$y = x^{2} + 7x +10$
Hint (d):
Look at parts (a) through (c). Remember to factor first to find the x-intercepts.

$y = x^{2} + 6x + 8$
Hint (e):
Look at parts (a) through (d).

$y = −x^{2} − 4x − 4$
Hint (f):
Look at parts (a) through (d). Remember to factor $−1$ out.

Check your predictions with your calculator.
Hint (g):
What is true about all of the equations where the parabola touches the x-axis at only one point?
Write a clear explanation describing how you can tell whether the equation of a parabola will touch the x-axis at only one point.

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