Y 4 4 y 4 0 4 4 4 0 4 x 4 answer y 3x 2 answer

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Unformatted text preview: "greater than inequality. For any inequality statement that is solved for y the solution will include: points above the boundary line for > or ≥ inequalities, points below the boundary line for < or ≤ inequalities, Unit 3: Day 5 notes - Linear Inequalities in Two Variables Page 4 of 4 exercise: Draw the graph of y ≤ − 5 x − 1 2 exercise: Draw the graph of 2x − 3y < 12 exercise: Write the inequality for each graph. y 4 -4 y 4 0 4 -4 -4 0 4 x -4 [Answer: y ≥ 3x − 2] [Answer: y < −x + 3] PRE-CALCULUS 11 Unit 3 – Day 6: QUADRATIC INEQUALITIES IN TWO VARIABLES GRAPHING INEQUALITIES IN TWO VARIABLES Like linear inequalities in two variables: • The points that make up the graph of an equation in two variables have coordinates that satisfy the equation, ∴ all the points not on the line do not satisfy the equation. • The line from the equation forms a boundary separating the "greater than" points from the "less than" points. example: Consider the quadratic function y = x2 − 6x + 5 • The points on the parabola have coordinates that satisfy the function's equation. • The points above the parabola have coordinates that satisfy y > x2 − 6x + 5 . • The points below the parabola have coordinates that satisfy y < x2 − 6x + 5 . y y > x2 − 6 x + 5 4 y = x2 − 6 x + 5 0 1 5 x y < x2 − 6 x + 5 −4 To graph the solution of a quadratic inequality in 2 variables: • Draw the boundary line. o Draw the line of the equation that corresponds to the inequality. o Use a solid line if points on the boundary satisfy the inequality; use a dashed/broken line if points on the boundary do not satisfy the inequality. • Determine the region with the points that satisfy the inequality. o Choose a point on one side of the boundary and check if its coordinates satisfies the inequality. o If the coordinates satisfy the inequality shade that region, otherwise shade the other region. Unit 3: Day 6 notes - Quadratic Inequalities in Two Variables Page 2 of 2 exercise: Draw the graph of y > x2 + 4x − 2 exercise: Draw the graph of y ≥ 5 − 2x2 exercise: Write the inequality for each graph. y 4 -4 y 4 0 4 -4 [Answer: y < 2x2 + 8x + 3] -4 0 4 -4 [Answer: y ≤ −x2 + 6x − 8] PRE-CALCULUS 11 Unit 3 – Day 7: QUADRATIC INEQUALITIES IN ONE VARIABLE A quadratic equation in one variable can be written in the form ax2 + bx + c = 0 . A quadratic equation in one variable can be solved graphically and algebraically. A quadratic inequality in one variable will have an inequality symbol instead of = . A quadratic inequality in one variable can be solved graphically and algebraically. SOLVING QUADRATIC INEQUALITIES IN ONE VARIABLE GRAPHICALLY example: Consider the quadratic function y = x2 − 6x + 5 • The roots of the associated quadratic equation are found at the points on the graph that are also on the x-axis where the...
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