Pre-AP Algebra 2
Unit 4 – Lesson 5 – Quadratic Formula and Discriminants
Objectives: The students will be able to:
 Prove the quadratic formula by completing the square.
 Use the quadratic formula to solve quadratic equations
 Use the discriminant to determine the nature of the roots and the information that it provides about the graph of
a quadratic function
Materials: Hw #4-4 answers overhead; tally sheets; pair work; homework #4-5
Time
5 min
15 min
Activity
Homework Review
Put up the answers to homework on the overhead for students to check. Pass around tally sheets.
Homework Presentation
Review the top 2 – 3 questions based on the tally sheets.
Direct Instruction
Proof of the Quadratic Formula:
(
(
(
)
(
)
)
)
√
√
√
√
30 min
Because this is true without using any specific numbers, this formula will work to solve any quadratic
equation in the form ax2 + bx + c = 0.
Pairwork
Practice solving by completing the square and by using the quadratic formula. This activity will lead
into using the discriminant to identify the number and type of solutions.
Homework # 4-5:
Pre-AP Algebra 2
4-5 Pairwork
Solve by completing the square and then solve by using the quadratic formula.
Completing the Square
Quadratic Formula
Completing the Square
Quadratic Formula
Do you get the same answers?
Which way is faster?
Solve each by using the quadratic formula. For each equation, state the number of solutions and
tell whether the solutions are real or complex, and, if real, whether the solutions are rational or
irrational. Also, look at the graph of the function to find the number of x-intercepts.
1.
Number of solutions:_____
Real or Complex:______________
Rational or Irrational:_______________
Number of x-intercepts:________
2.
Number of solutions:_____
Real or Complex:______________
Rational or Irrational:_______________
Number of x-intercepts:________
3.
Number of solutions:_____
Real or Complex:______________
Rational or Irrational:_______________
Number of x-intercepts:________
4.
Number of solutions:_____
Real or Complex:______________
Rational or Irrational:_______________
Number of x-intercepts:________
The discriminant of a quadratic equation gives you information about the type of roots that you
will get. The discriminant is
–
.
Write the quadratic formula here:
Where in the formula do you see the discriminant?
Looking back at the previous table, use the table below to summarize what information the
discriminant tells you.
Discriminant
and
is a
perfect square
and
is not a
perfect square
# of solutions Real or
complex
Rational or
irrational
x-intercepts on a graph
Pre-AP Algebra 2
Lesson 4-5 Homework
Name____________________________________
Review of Solving Quadratics
Solve each quadratic equation. You must use each method twice (factoring, taking square roots,
completing the square, and quadratic formula)
1.
2.
3. (
)
4.
5.
6.
7.
8.
9.
10.
(
)
Use the discriminant to determine the number and type of roots of each of the following equations.
Remember, you must have one side equal to 0 first.
11.
–
Discriminant:
Roots:
12.
Discriminant:
Roots:
13.
Discriminant:
Roots:
Discriminant:
Roots:
Discriminant:
Roots:
14.
15.
–
–