Answer:

Example:

Solve the quadratic inequality x2 – 4x > –3

Solution:

Step 1: Make one side of the inequality zero

x2 – 4x > –3

x2 – 4x + 3 > 0

Step 2: Factor the quadratic expression

x2 – 4x + 3 > 0

(x – 3)(x – 1) > 0

Step 3: Find the range of values of x which satisfies the inequality.

(x – 3)(x – 1) > 0 (y is positive): we choose the interval for which the curve is above the x-axis.

x < 1 or x > 3

Note: If the quadratic inequality was (x – 3)(x – 1) < 0 (y is negative), we would have chosen the interval for which the curve is below the x-axis i.e. 1 < x < 3

The following graphs show the solutions for x2 – 4x + 3 > 0 and x2 – 4x + 3