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Quadratic Inequalities

Quadratic Inequalities. Lesson 3.3. Definition. Recall the quadratic equation ax 2 + bx + c = 0 Replace = sign with <, >, ≤, or ≥ makes it a quadratic inequality Solving: Find where the equality occurs These values are the boundary numbers. Graphical Solutions.

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Quadratic Inequalities

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  1. Quadratic Inequalities Lesson 3.3

  2. Definition • Recall the quadratic equationax2 + bx + c = 0 • Replace = sign with <, >, ≤, or ≥ makes it a quadratic inequality • Solving: • Find where the equality occurs • These values are the boundary numbers

  3. Graphical Solutions • Graph of the quadratic y = ax2 + bx + c is a parabola • Extends upward or downward • Solution to y > 0 includes all x-values where graph isabove the axis • Solution to y < 0 includes x-values where graph isbelow the axis

  4. Try It Out • Given • Place in Y= screen, graph • Determine boundary values (zeros of equation) • Which values of x satisfy the inequality?

  5. or Another Version • Consider 2x2 > 16 • Create a graph of both sides of the inequality • Determine values of x which satisfy the equation, then the inequality

  6. Steps for Symbolic Solution • Write as an equation ax2 + bx + c = 0 • Solve resulting equation for boundary numbers • Use boundary numbers to separate number line into disjoint intervals • Make a table of test values • One value from each interval • Use this to specify which intervals satisfy the original inequality

  7. • • This is the interval Example Try x2 – 9 < 0 • Solve x2 – 9 = 0 • x = +3 or x = -3

  8. Using the Calculator Table • Place function in the Y= screen • Go to Table, ♦Y • Adjust start, incrementas needed, F2 • View intervals where results are • negative, • zero, • or positive x2 – 9 < 0

  9. Assignment • Lesson 3.3 • Page 195 • Exercises 1 – 39 odd

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