Chapter 8.6, Problem 4E

To determine

To choose: The correct option that is different one from other graph.

Answer to Problem 4E

The option C is different one from other graphs.

Explanation of Solution

The behavior of the graph of the parabola is U shaped curve that is open upward or downward where vertical symmetry can be drawn through the vertex of parabola at which the parabola is symmetric.

The parabola decreases until the vertex then starts increasing or the parabola increases until the vertex then starts decreasing

It can be seen from the first graph that it is form of the parabola whose vertex is $\left(0,0\right)$ since the parabola is symmetrical through the vertex and the parabola decreases until the vertex then starts increasing

Second graph is also a graph of parabola that is of quadratic equation whose vertex is $\left(0,-1\right)$ since the parabola is symmetrical through the vertex and the parabola increases until the vertex then starts decreasing.

It is difficult to find the vertex on third graph such that the graph increases gradually then after a point it increases at the increasing rate that does not matches with the behavior of the parabola.

Third graph is the graph of the exponential function.

Third graph is also a graph of parabola that is of quadratic equation whose vertex is $\left(0,2\right)$ since the parabola is symmetrical through the vertex and the parabola increases until the vertex then starts decreasing.

Thus, third graph is different one that means the option C is correct.