Straighten it first
Show on a big screenSome equations hide their degree, the highest power of x. Tidy them first. Tidy means straighten. Put every term on one side.
3x² = 5x − 1, as given.3x² = 5x − 1, as given.- Move every term to the left side. Each moved term changes sign.
- Gathered:
3x² − 5x + 1 = 0. a = 3,b = −5,c = 1.
The rule
Move every term to one side. Gather like terms, the ones with the same power of x. Then read the highest power of x.
A quadratic equation can be written as ax² + bx + c = 0, with a ≠ 0. This is the standard form. Here a ≠ 0 means a is not zero.
agoes with x².bgoes with x.chas no x.
If a = 0, the x² term is gone. The equation is linear when b is not 0.
| As given | Tidied | Degree | Name |
|---|---|---|---|
x² + 3 = 7x | x² − 7x + 3 = 0 | 2 | quadratic |
3x + 1 = x + 6 | 2x − 5 = 0 | 1 | linear |
x + 4 = x + 4 | 0 = 0 | none | no x left |
Take (x + 2)² = x² + 3x. The left side is x² + 4x + 4. Subtract x² + 3x from both sides. That leaves x + 4 = 0. It has no x² term, so it is not quadratic.
Now try it. Tap a term to move it across the = sign. Its sign flips. Move every term to the left. Then read the name.
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Try the lab to finish this lesson.