Answer
(a) True
(b) False
Work Step by Step
First of all because it is given that f(x) is a quadratic function , its graph is a parabola.
(a) this is true. because f(x)-c is a vertical transltion of graph of f(x), there is only one and one value of c that will move the vertex of the parabola to the axis.
(b) this is false. because f(x-c) is a horizontal translation of the graph of f(x). if f(x) has a double root, then f(x-c) will have a double root of any value of c; on the other hand if f(x) does not have a double root, then there is no value of c for which f(x-c) will have a double root.
