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Solving Quadratic Equations

There are two ways to solve a quadratic equation: the quadratic formula and by

factoring. There are advantages and disadvantages to each. In both cases, we must first

get the equation in the form ax

+ bx + c = 0 (get zero on one side). Also, in both cases,

these values of “x” we’re finding are the x-intercepts because we’re letting y = 0.

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The Quadratic Formula: If ax

+ bx + c = 0, then

(where a isn’t 0).

Advantage: It always works.

Disadvantage: Lots of places to make mistakes.

Factoring: If the quadratic can be factored, we can set (ax + b)(cx + d) = 0 and each piece

then equals zero

(ax + b) = 0 and (cx + d) = 0

Advantage: Easier than the quadratic formula.

Disadvantage: Doesn’t always work.

We’ve already seen where the quadratic formula can be useful, so let’s look at a situation

where we can factor.

Example 1:

a) Solve x

– 7x = –12 by factoring

b) Solve x

– 7x = –12 by the quadratic formula.

Graph of y = x

- 7x + 12

Notice:

1) Factoring, when possible, tends to be easier than using the

quadratic formula.

2) When you use the quadratic formula, you can tell if factoring is

possible because the value you get under the square root will be a

nice, square number.

3) Can you see the values of x you found on the graph to the left?

They are (3, 0) and (4, 0). (Where y = 0; the x-intercepts)

Solving Quadratic Equations