the figure shows the graph of y =(x-3)(x-5)(x-a). determine the value of a?

Question

answer options are:
a) 3
b) 4
c) 5
d) 7

Answer 1

The graph will cross the x-axis at each root (3, 5, and a) if they are all different. So, if the graph crosses the x-axis at 4, in addition to 3 and 5, then the answer is (b) 4. (Same with (d) 7, if the graph crosses the x-axis at 7.)

Otherwise, the graph should come down and touch the x-axis at one of x=3 or x=5, reversing direction and not just crossing it. In that case, you have the square of one of the roots. So, if the graph touches the x-axis at x=3 and reverses direction without crossing it, then you know that the equation has a factor of (x-3)^2 and the answer is (a) 3. (Same with (c) 5, if the graph touches the x-axis without crossing it at x=5.)

Answer 2

where's the figure.
the cubic has 3 roots, 3, 5, a. So these are the 3 places where it crosses the x-axis.

or else, it only crosses the x-axis once, and touches it another time. in this case a is 3 or 5. the single root is where it crosses and the double root, a, is where it touches.

Answer 3

Don't you think it would be nice if we could see the figure?
The answer is wherever the curve cuts the x-axis and not at 3 or 5.

Answer 4

y = (x - 3)(x - 5)(x - a)
problem is not complete . . even if y = 0