Quadratic Inequalities

You can solve a quadratic inequality algebraically by factoring.

Just like solving a quadratic equality we set it = to 0. we move the quadratic to the left side and let the right side of the inequality be 0.

The next step is to factor and solve each factor with the 0. remember the and or the or. And means the solutions are between the zeros or means they are outside the zeros.

Here is a graphical representation of an and solution: x2 – 4x ≤ 0

Algebraically the solution is 0 ≤ x ≤ 4

Here is a graphical representation of an or solution: x2 – 4x ≥ 0

Algebraically the solution is x ≤ 0 or x ≥ 4

Example y ≤ x2 +x + -6

Find zeros algebraically.

(x + 3) (x – 2) = 0 use equal to find the zeros by factoring.x + 3 = 0 or x – 2 = 0x = -3 or x = 2 these are my zeros and because it is an or problem I know it is going outside.

x2 + x – 6 ≥ 0 I moved the quadratic to the other side and flipped the inequality so I would know this was and or problem.

Algebraic solution x ≤ -3 or x ≥ 2

Practice:

2x2 – 11x – 16 ≤ 5