Solving Quadratic Inequalities
Solving Quadratic Inequalities
You will be able to:
1. Identify quadratic inequalities in one variable.
2. Solve quadratic inequalities graphically
Standard Form for a Quadratic Inequality in One
Variable:
ax + bx + c < 0
ax + bx + c > 0
ax + bx + c  0
ax + bx + c  0
To solve quadratic equations graphically:
• Graph both parabolas on the same coordinate plane.
• Determine the intersections, if they exist.
• Locate the portion of the y 1 graph below
the y 2 graph if the inequality is “less
than.” Locate the portion of the y 1 graph above
the y 2 graph if the inequality is “greater
than.”
• Determine the x -coordinates for this portion of the
graph.
- If the portion is to the left of the intersection, then
x is less than the x -coordinate of the intersection.
- If the portion is to the right of the intersection, then
x is greater than the x -coordinate of the intersection.
- If the portion is between the left and right
intersections, then x is greater than the x -coordinate
of the left intersection and less than the x -coordinate
of the right intersection.
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Algebra Buster can solve problems in these areas...
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simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values) |
|
factoring and expanding expressions |
|
finding LCM and GCF |
|
operations with complex numbers (simplifying, rationalizing complex denominators...) |
|
solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations) |
|
solving a system of two and three linear equations (including Cramer's rule) |
|
graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions) |
|
graphing general functions |
|
operations with functions (composition, inverse, range, domain...) |
|
simplifying logarithms |
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basic geometry and trigonometry (similarity, calculating trig functions, right triangle...) |
|
arithmetic and other pre-algebra topics (ratios, proportions, measurements...) |
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This limited time offer is only
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