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Chapter P: Prerequisite Information. Section P-7: Solving Inequalities Algebraically and Graphically. Objectives. You will learn about: Solving absolute value inequalities Solving quadratic inequalities Approximating solutions to inequalities Projectile motion Why:

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chapter p prerequisite information

Chapter P:Prerequisite Information

Section P-7:

Solving Inequalities Algebraically and Graphically

objectives
Objectives
  • You will learn about:
    • Solving absolute value inequalities
    • Solving quadratic inequalities
    • Approximating solutions to inequalities
    • Projectile motion
  • Why:
    • These techniques are involved in using a graphing utility to solve inequalities
vocabulary
Vocabulary
  • Union of two sets A and B
  • Projectile motion
solving absolute value inequalities
Solving Absolute Value Inequalities
  • Let u be an algebraic expression in x and let a be a real number with a ≥ 0.
    • If |u| < a, then u is in the interval (-a, a).
      • That is, |u| < a if and only if –a < u < a
    • If |u| > a, then u is in the interval (-∞, -a) or (a, ∞).
      • That is |u| > a if and only if u < -a or u > a
example 3 solving a quadratic inequality
Example 3:Solving a Quadratic Inequality
  • Solve x2 – x – 12 > 0
    • First, solve the equation x2 – x – 12 = 0
    • Graph the equation and observe where the graph is above zero.
example 4 solving another quadratic inequality
Example 4:Solving another quadratic inequality
  • Solve 2x2 + 3x ≤ 20
  • Again, solve the equation and graph
example 5 solving another quadratic inequality
Example 5:Solving another quadratic inequality
  • Solve x2– 4x + 1 > 0
  • This one we must do graphically because the equation does not factor.
  • Enter on your calculator: y = x2 – 4x + 1
  • We will use the trace key to observe where we have zeros.
example 6 showing there is no solution
Example 6:Showing there is no solution
  • Solve x2+ 2x + 2 ≤ 0.
    • Graph the equation. Where is the equation below the x-axis?
    • Use the quadratic formula to verify your answer.
example 7 solving a cubic inequality
Example 7:Solving a cubic inequality
  • Solve x3 +2x2 + 2 ≥ 0
  • Enter the equation in y =
  • Estimate where your zeros are and then use the zero trace function to find the values.
projectile motion
Projectile Motion
  • Suppose an object is launched vertically from a point s0 feet above the ground with an initial velocity v0 feet per second. The vertical position s (in feet) of the object t seconds after it is launched is:
  • s = -16t2 + v0t + s0
example 8 finding the height of a projectile
Example 8:Finding the height of a projectile
  • A projectile is launched straight up from ground level with an initial velocity of 288 ft/sec.
    • When will the projectile’s height above the ground be1152 ft?
    • When will the projectile’s height above the ground be at least 1152 ft?