Question

Which graph is defined by the function given bellow? Y = (x-2)(x+5)

Answer 1

Graph A

Explanation:

The first step is to expand the parentheses with FOIL:

`(x-2)(x+5)=x^2-2x+5x-10=x^2+3x-10`

Now, you can turn it into vertex form by completing the square:

`(x^2+3x+(9)/(4))-(9)/(4)-10=`

`(x+(3)/(2))^2-(49)/(4)`

This defines a parabola with a shift to the left of
`(3)/(2)` units and a shift down of
`(49)/(4)` or
`12 (1)/(4)` units. This describes graph A. Hope this helps!