Question

Write the quadratic function y = x2 + ax (assuming a is nonzero) in vertex form.

Answer 1

Try completing the square.

Answer 2

recall if you have \(x^2+bx\), then to complete the square you can add and subtract \(\large \left( \frac{b}{2}\right)^2 \)

Answer 3

Add and subtract?

Answer 4

\[ x^2+ax+\left( \frac{a}{2}\right)^2-\left(\frac{a}{2}\right)^2\\ ~ \\ =x^2+ax+\frac{a^2}{4}-\frac{a^2}{4} \\ ~ \\=\left( x+\frac{a}{2}\right)^2-\frac{a^2}{4}\]