CPM Homework Help : INT2 Problem 11-24

Rewrite $y = x^2 + 3x + 4$ in graphing form. Then use either equation to determine the $x$ -intercepts algebraically. What happens? Why?

Step 1:

Complete the square:

$y = (x + 1.5)^2 + 1.75$

Step 2:

Set $y$ equal to $0$ :

$0 = (x + 1.5)^2 + 1.75$
$-1.75 = (x + 1.5)^2$

Answer:

You cannot get a negative number from a square root, so there are no real solutions to either equation.
This means that the parabola never crosses the $x$ axis.