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

Start with the general equation of the quadratic in vertex form. It is U shaped and will open upward or downward depending on the value of "a." This particular graph produces a quadratic or a parabola.

y = a(x - b)^2 + c

"a" is the constant that will determine which way the parabola opens. It it is minus, the quadratic has a maximum at (b,c) assuming b and c are both greater than 0.

If a > 0 then (b,c) is a minimum and the parabola opens upward.
If a = 0 then the x^2 term does not exist and the parabola does not exist.