Quadratic Inequalities - Revision history

MathAdmin: /* Example */

2015-10-18T01:41:56Z

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MathAdmin at 01:41, 18 October 2015

2015-10-18T01:41:34Z

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==Introduction== In this section we will solve inequalities that involve quadratic functions. The approach can be summarized as moving ev..."

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Created page with "<div class="noautonum">__TOC__</div> ==Introduction== In this section we will solve inequalities that involve quadratic functions. The approach can be summarized as moving ev..."

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<div class="noautonum">__TOC__</div>
==Introduction==

In this section we will solve inequalities that involve quadratic functions. The approach can be summarized as moving everything onto one side of the inequality sign, preferably so the coefficient of <math>x^2</math> is positive, then find the x-intercept,
and use knowledge of whether the parabola opens up or down to solve the problem.

==Example==

Solve the inequality <math>3x^2 - 5x + 2 \ge 0</math>

Since all of the non-zero terms are already on the same side we can skip the first step. Now we need to look at the
discriminant. The discriminant is <math> (-5)^2 - 4(3)(2) = 1</math>. So there are two distinct x-intercepts(zeroes) and we can use the quadratic formula to find them.
By the quadratic formula the x-intercepts are <math> \frac{5 \pm\sqrt{1}}{2(3)} = \frac{5\pm 1}{6}<math>. So the two x-intercepts are <math> (1, 0), and (\frac{2}{3}, 0)</math>.

Since the coefficient of <math>x^2</math> is positive the parabola opens up. Thus, the answer is <math> (-\infty, \frac{2}{3}]\cup [1, \infty)</math>

[[Math_5|'''Return to Topics Page]]

@@ Line 11: / Line 11: @@
 Since all of the non-zero terms are already on the same side we can skip the first step. Now we need to look at the
 discriminant. The discriminant is <math> (-5)^2 - 4(3)(2) = 1</math>. So there are two distinct x-intercepts(zeroes) and we can use the quadratic formula to find them.
-By the quadratic formula the x-intercepts are <math> \frac{5 \pm\sqrt{1}}{2(3)} = \frac{5\pm 1}{6}</math>. So the two x-intercepts are <math> (1, 0), and (\frac{2}{3}, 0)</math>.
+By the quadratic formula the x-intercepts are <math> \frac{5 \pm\sqrt{1}}{2(3)} = \frac{5\pm 1}{6}</math>. So the two x-intercepts are <math> (1, 0), \text{ and } (\frac{2}{3}, 0)</math>.
 Since the coefficient of <math>x^2</math> is positive the parabola opens up. Thus, the answer is <math> (-\infty, \frac{2}{3}]\cup [1, \infty)</math>
 [[Math_5|'''Return to Topics Page]]

Quadratic Inequalities - Revision history

MathAdmin: /* Example */

MathAdmin at 01:41, 18 October 2015

MathAdmin: Created page with "__TOC__ ==Introduction== In this section we will solve inequalities that involve quadratic functions. The approach can be summarized as moving ev..."

MathAdmin: Created page with "
TOC
==Introduction== In this section we will solve inequalities that involve quadratic functions. The approach can be summarized as moving ev..."