Solving Quadratic Equations Page 2

The disadvantage to factoring is that it doesn’t always work. What do I mean by “work”? I

mean that sometimes there are x-intercepts that cannot be found by factoring because those

x-intercepts are not rational numbers. But, just because factoring doesn’t work, it doesn’t

mean that there are no x-intercepts. This is where the quadratic formula comes into play.

Example 2: Solve x

+ x – 3 = 0

Graph of y = x

+ x – 3

It’s hard to tell what the exact x-intercepts

are without the quadratic formula.

How do we know for certain there are no x-intercepts for a quadratic equation? Because the

quadratic formula will give us a negative underneath the square root.

Example 3: Solve x

= –x – 1

(Remember, you have to get “0” on one side first!)

Graph of y = x

+ x + 1

Notice there are no x-intercepts.

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