Question

What is the vertex form of `y=(-x+12)(2x-5)`?

Answer 1

Equation in vertex form is `-2(x-29/4)^2+361/8` and vertex is `(29/4,361/8)` or `(7 1/4,45 1/8)`.

Explanation:

This is the intercept form of equation of a parabola as the two intercept on `x`-axis are `12` and `5/2`. To convert it in vertex form we should multiply RHS and convert it to form `y=a(x-h)^2+k` and vertex is `(h,k)`. This can be done as follows.

`y=(-x+12)(2x-5)`

= `-2x^2+5x+24x-60`

= `-2(x^2-29/2x)-60`

= `-2(x^2-2×29/4×x+(29/4)^2)+(29/4)^2×2-60`

= `-2(x-29/4)^2+841/8-60`

= `-2(x-29/4)^2+361/8`

and hence vertex is `(29/4,361/8)` or `(-7 1/4,45 1/8)`.

graph{y-(-x+12)(2x-5)=0 [0, 20, 0, 50]}