Curriculum placement
Algebra 1. This describes the skill, not a learner estimate.
The quadratic formula
Use the quadratic formula and interpret the discriminant
Problem types
- Exact irrational quadratic solutions
- Count real quadratic solutions
- A quadratic with one real root
- Choose the quadratic formula solutions of a nonmonic equation
Builds on
- Completing the square
- Linear equations with letter coefficients · Useful idea
Choosing a parameter so that an equation has a given root or double root uses the discriminant.
- Which number systems stay closed · Useful idea
A root such as (−b + √d) / 2a is a rational number plus a nonzero rational multiple of √d. When √d is irrational, the closure rules make the whole root irrational.
Leads to
- Calculating with complex numbers
- How many times a line meets a curve
- Zeros and factors of a polynomial · Extend the idea
The quadratic formula gives zeros of a degree-two polynomial, and the discriminant tells whether a zero repeats.
Related skills
- Equations of circles · Shared foundations
Open the interactive map to explore lessons and skill connections.