The Quadratic Formula and the Discriminant: Solve and Predict

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Mathematics · Algebra II
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Page 2
The Quadratic Formula and the Discriminant:
Solve and Predict
Mathematics · Algebra II · Grades 10-12 · 50 minutes
Time needed
50 minutes (one class period)
Prep
Copy the 2-page worksheet (one per student). Write the quadratic formula and the
discriminant rules on the board.
Technology
None. Calculators are optional for arithmetic and square roots.
Student
independence
High. Students work alone, then compare with a partner.
Copies to make
One 2-page worksheet per student
Materials
Pencils, Worksheet, Whiteboard or chalkboard, Calculators (optional)
Goal for today: Students will use the discriminant to predict the number of real solutions of a quadratic equation and
will solve quadratic equations with the quadratic formula.
Before the bell
☐ Copy the worksheet, one per student (2 pages).
☐ Write on the board: For ax² + bx + c = 0, x = (−b ± √(b² − 4ac)) / (2a).
☐ Also write: Discriminant = b² − 4ac. If it is positive: 2 real solutions. If it is zero: 1 real solution. If it is
negative: no real solutions.
☐ Write the worked example: x² + 2x − 3 = 0 has a = 1, b = 2, c = −3. Discriminant = 4 + 12 = 16. x = (−2 ±
4)/2, so x = 1 or x = −3.
Say this to start
Good morning! Today students are working with the quadratic formula. First they predict how many solutions an
equation has, then they solve it, and finally they use the formula on a real-world falling-object problem. The formula
and an example are on the board, so everything students need is in front of them.


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Mathematics · Algebra II
SP-ALG2-002  ·  Free to print and use in your classroom  ·  substituteplans.com
Page 3
Run of show
Minutes
What you do
What students do
0–5
Take attendance. Hand out the worksheet and have
students put their names on it.
Write their names and look over the
worksheet.
5–13
Read the formula, the discriminant rules and the worked
example on the board aloud. Point out that a, b and c
include their signs.
Follow along and ask quick questions.
13–22
Tell students to complete the table at the top of the
worksheet (a, b, c, the discriminant and the number of real
solutions).
Fill in the table for four equations.
22–37
Tell students to solve problems 1–6 and the falling-object
problem 7. Walk the room and point stuck students to the
worked example.
Solve with the quadratic formula, showing
each step in the work boxes.
37–45
Read the table answers and problems 1–7 aloud from the
key. Students mark their own work. Then they answer
questions 8 and 9.
Check answers and complete the two
multiple-choice questions.
45–50
Tell students to write the exit ticket (question 10), then
collect all worksheets.
Answer question 10 and hand in the
worksheet.
If things go wrong
• If students get a negative number under the square root in problems 1–4 or 6, they should recheck the signs
of b and c. Only problem 5 has no real solutions.
• If students are unsure how to write a√b answers, accept decimals rounded to the nearest hundredth in
addition to the exact answers in the key.
• If a student gets stuck on 7, tell them to divide both sides by −16 first, which makes the numbers smaller.
• If the class finishes early, use the early finisher list.
Early finishers
• Make up a quadratic equation with discriminant 0. Prove it by computing b² − 4ac.
• Solve x² + 4x + 7 = 0 using complex numbers. (Hint: the discriminant is −12 and √−12 = 2i√3.)
Support and challenge
• Support: Let students write a, b and c on the line above each equation before substituting, and use a
calculator for arithmetic.
• Challenge: Ask students to find the value of k that makes x² + 6x + k = 0 have exactly one real solution.


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Mathematics · Algebra II
SP-ALG2-002  ·  Free to print and use in your classroom  ·  substituteplans.com
Page 4
Notes for the teacher (you fill this in)
Jot a few lines before you leave. A full Daily Sub Report is in the free Sub Survival Kit at SubstitutePlans.com.
How far the class got / what to pick up next:
Students who were especially helpful:
Anything the teacher should know: