CPM Homework Help : INT2 Problem 12-37

Without graphing, determine if the graph of each equation below has zero, one, or two $x$ -intercepts. Then describe the roots of each quadratic function. Show all work.

Hint:

The graphs of these equations are all parabolas. To find the $x$ -intercepts, let $y = 0$ and solve using the Quadratic Formula or factoring and the Zero Product Property.

$y = 6x^2 + 7x − 20$
Hint (a):
$0 = (3x - 5)(x + 4)$
Answer (a):
Two intercepts.

$y = x^2 - 8x + 16$
Hint (b):
$0 = (x - 4)^2$

$y = 2x^2 + x + 3$
Answer (c):
No intercepts.

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