A quadratic function is a function of the form [tex]f(x)=ax^2+bx+c[/tex]. The vertex, [tex](h,k)[/tex] of a quadratic function is determined by the formula: [tex]h= \frac{-b}{2a} [/tex] and [tex]k=f(h)[/tex]; where [tex]h[/tex] is the x-coordinate of the vertex and [tex]k[/tex] is the y-coordinate of the vertex. The value of [tex]a[/tex] determines if the parabola opens upward or downward; if[tex]a[/tex] is positive, the parabola opens upward and the vertex is the minimum value, but if [tex]a[/tex] is negative the graph opens downward and the vertex is the maximum value. Since the quadratic function only has one vertex, it could not contain both a minimum vertex and a maximum vertex at the same time.
