We need to analyze the following statement, telling if it is true or false:
A quadratic function can have both a maximum value and a minimum value.
Notice that a quadratic function can be written in the form:
[tex]f(x)=ax²+bx+c[/tex]with a, b, and c constants.
The graph of a quadratic function is a parabola. When the constant a is positive, a > 0, the parabola opens upwards and the function has a minimum.
When the constant a is negative, a < 0, the parabola opens downwards and the function has a maximum.
Therefore, it has a maximum OR a minimum. It can't have both.
Answer: False
