Y= (x- 3) (x+5) find vertex, min or max, x-intercepts, and y- intercepts show your work !

First, you want to do the FOIL method to expand the the equation. You get:

y = x² + 2x - 15

Now to find the vertex, you use this equation:

Vertex: x = - b / 2a
where the equation is in the form y = ax² + bx + c. Plug in the information needed given by this new equation. 

x = - 2 / 2(1)
= - 2 / 2
= - 1

Now we plug in - 1 for x. 

 y = (- 1)² + 2(- 1) - 15
y = 1 - 2 - 15
y = - 1 - 15
y = - 16.

Your vertex is (- 1, - 16).

For the y-intercept, plug in zero for x and solve. 
y = (0)² + 2(0) - 15
y = 0 + 0 - 15
y = - 15. 

Your y-intercept is (0, - 15). 

For the x-intercept, plug in zero for y and solve. Easy way to do this is just plug it into your original equation and set each binomial equal to zero. 
x - 3 = 0
x = 3

x + 5 = 0 
x = - 5. 

Your x-intercepts are at (- 5, 0) and (3, 0). 

Graph included for proof of these answers.