# What is the vertex form of y= (x-3)(x-4) ?

Jan 9, 2016

Multiply out and then complete the square to find the vertex form.

#### Explanation:

y = (x - 3)(x - 4)

y = ${x}^{2}$ - 3x - 4x + 12

y = ${x}^{2}$ - 7x + 12

y = 1(${x}^{2}$ - 7x + m - m) + 12

m = ${\left(\frac{b}{2}\right)}^{2}$

m = ${\left(- \frac{7}{2}\right)}^{2}$

m = $\frac{49}{4}$

y = 1(${x}^{2}$ - 7x + $\frac{49}{4}$ - $\frac{49}{4}$) + 12

y = 1${\left({x}^{2} - \frac{7}{2}\right)}^{2}$ - $\frac{1}{4}$

The vertex form of y = (x - 3)(x - 4) is y = 1${\left({x}^{2} - \frac{7}{2}\right)}^{2}$ - $\frac{1}{4}$

Below I have included 2 problems that you may do to practice yourself with the completion of square technique.

a) y = (2x + 5)(x - 6)

b) y = $3 {x}^{2}$ + 7x - 9