Warm Up Quiz 1

Use the quadratic formula to solve the equation.

Warm Up Quiz 1 - SOLUTIONS -

Use the quadratic formula to solve the equation.

Warm Up Quiz 2

Find the discriminant and use it to determine the type and the number of solution(s) of below equation.

Warm Up Quiz 2 - SOLUTIONS -

Find the discriminant and use it to determine the type and the number of solution(s) of below equation.

Two imaginary solutions or No real solutions.

Quadratic Inequalities

Lesson #9 of Unit 1: Quadratic Functions

and Factoring Methods (Textbook Ch1.9)

Learner Goal

Using a table, algebraically, graphing quadratic inequalities to solve for x values.

REFRESHER: Graphing a Standard Form

To graph a quadratic function in standard form …

1) First, find the x-value of its vertex using the formula ,

2) then use it to find the y-value of the vertex by plugging it in,

3) and use the value of c as the y-intercept,

4) finally find a third point that has same y-value as the y-intercept but on the opposite side of axis of symmetry.

Graph the function.

Group Discussion

1) Graph .

2) Plot (0, 0), (-4, 0), (0, -2), (-2, -4)

on the same grid.

3) Plot (0, -6), (-5, 0), (-4, -4), (2, 0)

on the same grid.

4) What is the common feature of the set of points for the 2)?

5) What is the common feature of the set of points for the 3)?

6) Which set satisfies the inequality ?

Graphing a Quadratic Inequality

The difference between graphing a quadratic equation and quadratic inequality is that a graph of quadratic inequality is NOT just a curved line but it’s a region that is created by a curved line, and the line itself could be excluded from the solution as well. To find which region is the solution, we use a test point. (0, 0) is usually a good test point.

Example)

Trying (0, 0) for the inequality, we get

which is true, so the region including (0, 0) is the solution. Also, the inequality does not include equal sign, so the line is dotted instead of solid.

Text p.66

Graph the inequality

(0, 0)

Graphing a System of Quadratic Inequality

Graphing a system of quadratic inequalities is very similar to graphing a quadratic function by itself. The only difference is that we will be shading the area where the solutions are. Any solution to one function must also be a solution to the other functions in the system. Try to look for the area where the two graphs overlap.

Example) y ≤ -x2 + 4 and y > x2 – 2x – 3

Step 1 – Graph y ≤ -x2 + 4 (BLUE) Step 2 – Graph y > x2 – 2x – 3 (GREEN)

Step 3 – Find the region where two graphs

overlaps. (BLUE + GREEN)

Text p.67

Graph the system of inequalities consisting of and .

Solving a Quadratic Inequality by Graphing

Find the graph’s x-intercepts by letting y = 0 and using the quadratic formula to solve for x. Then sketch a parabola using x-intercepts.

Example) 2x2 + x – 4 ≥ 0

Text p.68

Solve the inequality using a graph.

Solving a Quadratic Inequality by Algebraically

Write and solve the equation obtained by replacing inequality signs (<, >, ≤, and ≥ )with equal sign (=). Find the critical x-values of the inequality by solving quadratic equation. Plot the critical x-values on a number line then test an x-values in each interval to see if it satisfies the inequality.

Example) Solve x2 – 3x > 15

x2 – 2x=15

x2 – 2x – 15 = 0

(x+3)(x – 5) = 0

x= -3 or x = 5

Text p.66

Solve the inequality algebraically.

Suggested Problems

Day 1: Workbook p.19 - 21

8, 9, 11, 12

Day 2: Workbook p.19 – 21

20, 22, 23, 24

Suggested Problems - SOLUTIONS -

Day 1: Workbook p.19 – 21: Graph the inequality

8) 9)

11) 12)

Suggested Problems - SOLUTIONS -

Day 2: Workbook p.19 – 21: Graph the system of inequalities.

20) 22)

Workbook p.19 – 21: Solve the inequality algebraically.

23) 24)