### Home > INT2 > Chapter 11 > Lesson 11.1.2 > Problem11-24

11-24.

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

Complete the square:

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

Set $y$ equal to $0$:

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

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.