Question

Explain why the graph of quadratic function could not contain both a minimum vertex and a maximum vertex at the same time.

Answer 1

A quadratic function is a function of the form $f(x)=ax^2+bx+c$. The vertex, $(h,k)$ of a quadratic function is determined by the formula: $h= \frac{-b}{2a}$ and $k=f(h)$; where $h$ is the x-coordinate of the vertex and $k$ is the y-coordinate of the vertex. The value of $a$ determines if the parabola opens upward or downward; if$a$ is positive, the parabola opens upward and the vertex is the minimum value, but if $a$ 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.