Cogito
Integrated Math 2 · Chapter 2 · Lesson 2
The Quadratic Formula
A method that always works.
12 problems · about 22 minutes · A-REI.B.4
What this lesson teaches
The student solves quadratics with the formula and uses the discriminant to predict the roots.
- The quadratic formula solves every quadratic.
- The discriminant predicts two real roots, one, or none.
- Try factoring first; use the formula when it stalls.
Warm Up
Straightforward practice. Get the method working first.
5 problemsx² + 3x + 2 = 0. What is the discriminant?
Answer 1
Why 1.
A negative discriminant means what about the graph?
Answer The parabola never crosses the x-axis.
Why It misses the axis entirely.
x² − 6x + 5 = 0. Discriminant?
Answer 16
Why 36 − 20.
Same equation. Larger root?
Answer 5
Why (6 + 4) ÷ 2.
x² − 4x + 4 = 0. Discriminant?
Answer 0
Why 16 − 16.
Build It Up
The same ideas with more to keep track of.
3 problemsHow many distinct real roots does that have?
Answer 1
Why A zero discriminant.
x² + x + 3 = 0. Discriminant?
Answer -11
Why 1 − 12.
How many real roots does that have?
Answer 0
Why A negative discriminant.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each discriminant by what it predicts.
Answer Two real roots: Discriminant 25, Discriminant 3 · No real roots: Discriminant negative 9, Discriminant negative 1
Why Only the sign matters.
2x² − 8x + 6 = 0. Larger root?
Answer 3
Why Divide through by 2 first.
The Discriminant: x² − 4x + 1 = 0. What is the discriminant?
Answer 12
Why 12.
The Prediction: x² + 2x + 5 = 0. What is the discriminant?
Answer -16
Why −16, so no real roots.