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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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