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Solving Quadratic Inequalities Algebraically
• MM2A4. Students will solve quadratic equations and inequalities
in one variable. • d. Solve quadratic inequalities both graphically and algebraically,
and describe the solutions using linear inequalities.
Write the original inequality as an equation.
Write the equation in standard form by setting it equal to 0.
Factor.
Use the zero product property, set each parentheses equal to 0 and solve for the critical x-value.
Plot the points on a number lie and test points in each interval.
x2 – 4x – 3 > 0
To write the solution:
If the original equation contains:
≤ <: And, the solutions overlap“Less Thand”
≥ >: Or, the solutions go opposite“Greator”
x2 – 5x – 14 > 0Write the original inequality as an equation.
Write the equation in standard form by setting it equal to 0.
Factor.
Use the zero product property, set each parentheses equal to 0 and solve for the critical x-value.
Plot the points on a number lie and test points in each interval.
2x2 – 18 > 0Write the original inequality as an equation.
Write the equation in standard form by setting it equal to 0.
Factor.
Use the zero product property, set each parentheses equal to 0 and solve for the critical x-value.
Plot the points on a number lie and test points in each interval.
12x2 + 5x – 25 < 0Write the original inequality as an equation.
Write the equation in standard form by setting it equal to 0.
Factor.
Use the zero product property, set each parentheses equal to 0 and solve for the critical x-value.
Plot the points on a number lie and test points in each interval.
x2 + 2x – 3 > 0Write the original inequality as an equation.
Write the equation in standard form by setting it equal to 0.
Factor.
Use the zero product property, set each parentheses equal to 0 and solve for the critical x-value.
Plot the points on a number lie and test points in each interval.
