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

Your explanation should be 3-4 sentences and include at least 6 of the following words/phrase.

-parabola

- u-shaped graph

- vertex

- minimum

- maximum

- y-value of the vertex

- x-value of the vertex

- quadratic function

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.