Question

. How do you change from vertex form, f(x) = a(x-h)² + k, to standard form,
y = ax²+bx+c?

Answer 1

To convert a quadratic form y=ax²+bx+c form to vertex form, y=a(x-h)² + k you use the process of completing the square.

Answer 2

To change from vertex form to standard form, expand the squared term (a(x-h)^2), distribute the 'a', add the 'k' term, and simplify to get y = ax^2 - 2ahx + (ah^2 + k), which corresponds to y = ax^2+bx+c.

Step-by-step explanation:

Changing from vertex form, f(x) = a(x-h)^2 + k, to standard form, y = ax^2+bx+c, involves expanding the squared term and simplifying. Here is the step-by-step process:

1. Expand the squared term: a(x-h)^2 = a(x^2 - 2hx + h^2).
2. Distribute the 'a' across the terms in the parentheses: ax^2 - 2ahx + ah^2.
3. Add the 'k' term to the expression: ax^2 - 2ahx + ah^2 + k.
4. Combine like terms if necessary. In most cases, this will not be needed as 'h' and 'k' are part of the vertex form. Your final equation will look like y = ax^2 - 2ahx + (ah^2 + k).

The coefficients 'a', '-2ah', and '(ah^2 + k)' in the expanded form correspond to the 'a', 'b', and 'c' in the standard form respectively.