Looking at the function f(x), it is in the factored form, so we can easily find the zeros of the function (that is, the x-intercepts) by equating each factor to zero:
[tex]\begin{gathered} x-a=0\rightarrow x=a\\ \\ x-b=0\rightarrow x=b \end{gathered}[/tex]The x-coordinate of the vertex is given by the average value of the zeros:
[tex]\begin{gathered} x_v=\frac{x_1+x_2}{2}=\frac{a+b}{2}\\ \\ y_v=f(x_v)=(\frac{a+b}{2}-a)(\frac{a+b}{2}-b)=(\frac{-a+b}{2})(\frac{a-b}{2})=-\frac{(a-b)^2}{4} \end{gathered}[/tex]And the y-intercept can be found by using x = 0:
[tex]\begin{gathered} f(0)=(0-a)(0-b)\\ \\ f(0)=ab \end{gathered}[/tex]So the graph of this quadratic equation is given by:
