From the graph, we can conclude the following points:
1. Number of zeros = 4 ( As the graph intersects or touches the x axis at 4 points.)
2. Number of turning points are 6. ( As there are 3 minimums and 3 maximums)
3. Number of zeros with even powers are 3. ( As the graph touches the x axis at 3 points)
Among all the four options, only the first option fulfills all the above points.
The above function has 4 zeros at
The above function has 3 even zeros
Now, number of turning points for the above function is given as:
Turning points = Number zeros + Number of even zeros - 1 = 4 + 3 - 1 = 6
Therefore, the correct option is option 1.
a is the correct answer.
f(x ) (x -a )2(x-)(x - c)
in the graph you can see that the graph of the given function has four x-intercepts. one of them is 0 (choice d is incorrect, because factor x is not present), and denote rest as a, b, c, consecutively. at points 0, a and c function doesn't change sign, this means that factors x, (x-a), (x-c) have even degrees (choices b and c are incorrect, because in these options just two or three factors have odd degree). at point b function changes values from negative to positive, then the factor (x-b) should have odd degree. choice a is correct choice.