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Course covering algebra, calculus, and mathematical reasoning, develop analytical skills and prepare students for complex, higher-level mathematical challenges.

Advanced Math

Course covering algebra, calculus, and mathematical reasoning, develop analytical skills and prepare students for complex, higher-level mathematical challenges.

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Apr 4, 2026
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Video Details

Understanding the Quadratic Formula gLink to understanding-the-quadratic-formula-g

In this lesson, we solve equations of the form:

ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0

using the quadratic formula:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac​​

Key IdeaLink to understanding-the-quadratic-formula-g-key-idea

The expression under the square root is called the discriminant:

Δ=b2−4ac\Delta = b^2 - 4acΔ=b2−4ac

It determines the number and type of solutions.

You will learn

What you'll learnLink to understanding-the-quadratic-formula-g-what-you-ll-learn

  • How to identify coefficients aaa, bbb, ccc
  • How to compute the discriminant Δ=b2−4ac\Delta = b^2 - 4acΔ=b2−4ac
  • When Δ>0\Delta > 0Δ>0, there are two real solutions
  • When Δ=0\Delta = 0Δ=0, there is exactly one solution x=−b2ax = -\frac{b}{2a}x=−2ab​
  • When Δ<0\Delta < 0Δ<0, solutions are complex x=−b±i∣Δ∣2ax = \frac{-b \pm i\sqrt{|\Delta|}}{2a}x=2a−b±i∣Δ∣​​

ExampleLink to understanding-the-quadratic-formula-g-example

Solve:

2x2+3x−2=02x^2 + 3x - 2 = 02x2+3x−2=0 x=−3±32−4(2)(−2)2⋅2=−3±254=−3±54x = \frac{-3 \pm \sqrt{3^2 - 4(2)(-2)}}{2 \cdot 2} = \frac{-3 \pm \sqrt{25}}{4} = \frac{-3 \pm 5}{4}x=2⋅2−3±32−4(2)(−2)​​=4−3±25​​=4−3±5​ x=12orx=−2x = \frac{1}{2} \quad \text{or} \quad x = -2x=21​orx=−2

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Chapters

  • –Intro
  • –Outro
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