Question 447583

{{{y=(x-4)(x+2)}}}

You know two points on the graph; 
(4,0) and (-2,0), 

for those are the {{{x -intercepts}}} you stated above

Since parabolas are {{{always}}} symmetrical, you know that the {{{x}}} coordinate of the vertex {{{must}}} be {{{exactly}}}{{{ half}}}{{{ way}}} between these two coordinates(since they have the same {{{y}}} value), somewhere along the line {{{x=1}}}

plug {{{1}}} into the equation, and see what value you get for {{{y}}}:

{{{y = (1-4)(1+2)}}}

{{{y = -3(3)}}}

{{{y = -9}}}

so, the vertex is at (1,-9)