Graphing and Solving Quadratic Inequalities in Two Variables: A Step-by-Step Guide

Graphing and Solving Quadratic Inequalities in Two Variables: A Step-by-Step Guide

• 1.
  PLOT THE FOLLOWING POINTS (𝟎,𝟎) (𝟏,𝟎) (𝟎,𝟏) (−𝟐,𝟒) (𝟒,−𝟐) (𝟓,𝟖) (𝟑,𝟕) (−𝟑,−𝟕) (𝟔,𝟎)
• 2.
  Solves Quadratic Inequalities (Two Variables)
• 3.
  Learning Objectives At theend of the lesson, the learners should be able to: • Identify the boundary graph of a quadratic inequality in two variables. • Represent the solution region of quadratic inequalities on the coordinate plane. • Interpret the shaded region and determine whether given points satisfy the inequality.
• 4.
  There are quadraticinequalities that involve two variables. These inequalities can be written in any of the following forms. 𝑦 >𝑎𝑥2 +𝑏𝑥+𝑐 𝑦 <𝑎𝑥2 +𝑏𝑥+𝑐 𝑦 ≥ 𝑎𝑥2 +𝑏𝑥+𝑐 𝑦 ≤ 𝑎𝑥2 +𝑏𝑥+𝑐 where are real numbers and
• 5.
  EXAMPLES 𝑦 >2𝑥2 − 5𝑥+1 𝑦 <𝑥2 +3 𝑥 +2 𝑦 + 9 ≥ − 4 𝑥2 𝑦 −7 𝑥 ≤ 2 𝑥2
• 6.
  The solution setof quadratic inequalities in two variables can be determined graphically. To do this, write the inequality as an function, then show the graph. The graph of the resulting parabola will be used to graph the inequality. REMEMBER THIS!
• 7.
  EXAMPLE Example 1: Findthe solution set of Solution: Write the inequality to its corresponding equation Construct table of values for -5 -4 -3 -2 -1 0 1 2 12 6 2 0 0 2 6 12
• 8.
  Use these pointsto graph a parabola. (𝟎,𝟖) 𝟖<𝟐FALSE (𝟎,𝟎) 𝟎<𝟐TRUE (−𝟐,−𝟑) −𝟑<𝟔− 𝟔 −𝟑<𝟒−𝟔+𝟐 −𝟑< 𝟎 TRUE (−𝟔,𝟕) −𝟔<𝟕𝟐TRUE
• 9.
  The shaded region arethe solution set
• 10.
  EXAMPLE Example 2: Findthe solution set of Solution: Write the inequality to its corresponding equation 𝐲 ≥𝟐 𝒙𝟐 −𝟑 𝒙 +𝟏 𝐲=𝟐 𝒙𝟐 −𝟑 𝒙 +𝟏 Construct table of values for -3 -2 -1 0 1 2 3 4 28 15 6 1 0 3 10 21
• 11.
  Use these pointsto graph a parabola. 𝐲 ≥ 𝟐 𝒙𝟐 −𝟑 𝒙 +𝟏 (𝟏,𝟑) 𝟑≥ 𝟐− 𝟑+𝟏 FALSE (−𝟒 ,𝟔) (𝟔,𝟔) TRUE (−𝟑,−𝟏) 𝟑≥ 𝟑−𝟑 𝟑 ≥ 𝟎 𝟔≥𝟐(𝟑𝟔)−𝟏𝟖+𝟏 𝟔≥𝟕𝟐−𝟏𝟖+𝟏 𝟔 ≥ 𝟓𝟓 FALSE 𝟔≥𝟐(𝟏𝟔)+𝟏𝟐+𝟏 𝟔≥𝟑𝟐+𝟏𝟐+𝟏 𝟔 ≥ 𝟒𝟓 FALSE −𝟏≥ 𝟐(𝟏)+𝟑+𝟏 −𝟏 ≥ 𝟐+𝟑+𝟏 −𝟏 ≥ 𝟔
• 12.
  Use these pointsto graph a parabola. 𝐲 ≥ 𝟐 𝒙𝟐 −𝟑 𝒙 +𝟏 The shaded region are the solution set
• 13.
  1. Find thesolution set of then graph. YOUR TURN! 2. Determine whether or not each of the following points is a solution of the inequality . Justify your answer.
• 14.
  THANK YOU!