This week in Precalculus 11, we learned about quadratic inequalities and how to solve them. A quadratic inequality is when the equation is greater than 0 (x > 0), greater than or equal to 0 (x ≥ 0), less than 0 (x < 0), less than or equal to 0 (x ≤ 0), or equal to 0 (x = 0).
To solve a quadratic inequality, you have to make sure that one side is zero. If one side is not zero, then you have to move all the numbers to one side to make it zero.
Ex.
4 > x2 – 3x
0 > x2 – 3x – 4
Once all the terms are on one side and the other side is zero, you have to solve for x.
Ex.
0 > x2 – 3x – 4
0 > (x – 4)(x + 1)
x = 4 x = -1
A fast way to find the solution is to imagine a graph and to imagine the x-axis as the 0. We know that the x-intercepts are 4 and -1 and that a is positive, so the parabola will open up. Since 0 is greater than the x’s, we know that we have to find the inequalities for x when it’s above the x-axis. We can now establish that x < -1 and x > 4.