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# Identifying Characteristics of Quadratic Functions

## Identifying Characteristics of Quadratic Functions 1.12 - Solution

Go through the statements one at a time.
1. An absolute maximum means that the curve has its highest point at its vertex. That $g(x)$ has a maximum point is then true.

2. The statement that $f(x)$ has a vertex is true, because there is a point where the functions changes from decreasing to increasing.

3. A negative $x^2$-term gives a sad mouth according to the direction of a quadratic function. Since it's true that $g(x)$ has an absolute maximum, it's also true that it has a negative $x^2$-term.

4. The function $f(x)$ has an absolute minimum point, and, thus, a minimum value. Then, it continues infinitely far upwards, so it never reach any maximum value. Therefore, the statement is false.

5. Because the axis of symmetry goes through the minimum point, and is on the negative $x$-axis for $f(x)$ the line of symmetry can not have the positive $x$-value $5.$ So this claim is false.