College Algebra / Unit 6 Alg 329 worked example, 60 to 90 seconds
Converting General to Standard Form
The idea
Converting a quadratic function to standard form means completing the square on the function — grouping the x-terms, adding and subtracting the completing constant, and folding the square.
In practice
Convert f(x) = x² − 4x + 3. Group the x-terms: (x² − 4x) + 3. Half of −4 is −2; its square is 4. Add and subtract it inside the story: (x² − 4x + 4) + 3 − 4. Fold the perfect square: (x − 2)² − 1. The vertex (2, −1) now reads on sight, and the check runs both ways — expanding (x − 2)² − 1 returns x² − 4x + 3, and the vertex formula agrees: h = 4/2 = 2, k = f(2) = −1. On a function, the balance move changes: there is no other side to add to, so whatever is added is subtracted in the same line, and the function's value never moves.
Where people slip
Add and subtract on the same side; a function has no second side to balance against.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
- Nothing. This is a starting point.
Unlocks
- Nothing yet depends on this.
Something wrong in this lesson? Flag it · Sources for College Algebra