To solve quadratic inequalities: 1. Express the inequality in standard form ax^2 + bx + c > 0. 2. Determine the boundary points by setting the equation equal to 0 and solving for x. 3. Set intervals to the left and right of the boundary points. 4. Pick a test point in each interval and check if it makes the inequality true. 5. Write the solution intervals.

1. SOLVING QUADRATIC
INEQUALITIES

2. WOODGROVE
BANK 2
A quadratic inequality is a mathematical sentence in the form of ax2 +
bx + c > 0, that relates a quadratic expression using the inequality symbols
≠, <, >, ≤, or ≥.
To solve for quadratic inequalities,
a. express the inequality in standard forn;
b. determine the boundary points;
c. set the intervals that will represent values to the left and right of the
boundary points;
d. pick a test point for each interval and check which will make the
inequality statement true; then
e. write the solution for the inequality.

3. WOODGROVE
BANK 3
Example 1: Solve for the quadratic inequality of x2 + 2 ≥ 3x.
ax2 + bx + c > 0
a. x2 + 2 ≥ 3x
x2 – 3x + 2 ≥ 0
b. x2 – 3x + 2 = 0
(x – 2)(x – 1) = 0
x – 2 = 0 x – 1 = 0
x = 2 x = 1
The boundary points are 1 and 2. The graph shows the possible
interval solutions of the inequality. Since x can be equal to 1 or 2, there are
possible intervals which illustrated as (-∞, 1], [1, 2], [2, +∞).

4. WOODGROVE
BANK 4the
The solution to x2 + 2 ≥ 3x are the values of x that will
make the product of the factors x – 1 and x – 2 greater than or
equal to zero. We need to identify the interval/s that gives a result
with positive sign.
Thus the solutions are the intervals (-∞, 1] ∪ [2, +∞).