The Quadratic Formula in Action
Plug in a, b, and c. Watch the formula simplify to the roots.
Equation
y = -5^2 - 4*2*x
Graph
Table
| x | y |
|---|---|
| -10 | 105 |
| -9 | 97 |
| -8 | 89 |
| -7 | 81 |
| -6 | 73 |
| -5 | 65 |
| -4 | 57 |
| -3 | 49 |
| -2 | 41 |
| -1 | 33 |
| 0 | 25 |
| 1 | 17 |
| 2 | 9 |
| 3 | 1 |
| 4 | -7 |
| 5 | -15 |
| 6 | -23 |
| 7 | -31 |
| 8 | -39 |
| 9 | -47 |
| 10 | -55 |
What this lesson covers
What you do
You shape the function y = b^2 - 4*a*x and watch the graph answer.
Challenges to clear
- Set a = 1 and b = 2. The x-axis here is c: at c = 1 the discriminant is 4 − 4 = 0 — ONE repeated root.
- Same a, b: at c = −3, D = 4 + 12 = 16 > 0 — TWO distinct roots.
- Set the leading coefficient a to 2.
- The x-axis here is c. Slide b until the discriminant hits zero at c = 2 — b² = 4ac means ONE repeated root.
Check yourself
What does a positive discriminant (D > 0) indicate about the roots of the quadratic equation?
If the discriminant is zero (D = 0), how many real roots does the equation have?
- The equation has two distinct real roots. — correct
- The equation has one repeated real root.
- The equation has no real roots.
- The equation has complex conjugate roots.
- Two distinct real roots.
- One repeated real root. — correct
- No real roots.
- Infinitely many roots.
Think about it
- D = b² − 4ac decides the roots: D > 0 two roots, D = 0 one root, D < 0 none. With a=1, b=2, c=1: what is D?