Question

GROUP (ax² + bx) written in VERTEX FORM f(x) = a(x - h)² + k. If 'a' ≠ 1, how can you express it to have a( x² + bx) format?

a) Factor out 'a' from the equation.
b) Perform polynomial long division to simplify.
c) Use the quadratic formula.
d) Factor out 'b' from the equation.

Answer 1

To express a quadratic expression in the form ax² + bx in vertex form when 'a' is not equal to 1, factor out 'a' from the quadratic equation, which then allows for completing the square to reach vertex form.

Step-by-step explanation:

The question involves converting a quadratic expression in the standard form, ax² + bx, to the vertex form, f(x) = a(x - h)² + k. When 'a' ≠ 1, to achieve this, one should factor out 'a' from the quadratic and linear terms to isolate the x² term. This aligns with option (a) Factor out 'a' from the equation. After factoring out 'a', completing the square can be used to transform the equation into vertex form.