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Lesson 1 of 5

Introduction to Quadratics

A quadratic equation is any equation where the highest power of x is 2. They model curves, projectile paths, and much more.

Core Concept

Standard Form

A quadratic equation in standard form looks like:

ax² + bx + c = 0

Where a ≠ 0 (if a = 0, it's linear, not quadratic), and a, b, c are constants.

Identifying Parts

Identifying a, b, and c

2x² + 5x − 3 = 0 → a = 2, b = 5, c = −3
x² − 9 = 0 → a = 1, b = 0, c = −9
−3x² + x = 0 → a = −3, b = 1, c = 0
x² + 4x + 4 = 0 → a = 1, b = 4, c = 4

Important: Always rearrange to = 0 before identifying a, b, c.

Solutions

How Many Solutions?

A quadratic equation can have:

2
Two real solutions

Graph crosses x-axis twice

1
One repeated solution

Graph touches x-axis once

0
No real solutions

Graph doesn't cross x-axis

We determine which case applies using the discriminant (covered in Lesson 2-4).

Rearranging

Putting a Quadratic in Standard Form

Rearrange 3x² = 7x − 2 into standard form and identify a, b, c.

1. Move everything to one side:
2. 3x² − 7x + 2 = 0
3. a = 3, b = −7, c = 2

Your Turn

Try It Yourself

Q1. Identify a, b, c in 5x² − 3x + 8 = 0.

Show Answer

a = 5, b = −3, c = 8

Q2. Rearrange 4x = x² + 3 into standard form.

Show Answer

x² − 4x + 3 = 0 (a = 1, b = −4, c = 3)

Key Takeaways

1-Minute Summary

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