Quadratic functions and their graphs

Question

Let f(x)=ax²+bx+c be a quadratic function with a > 0 whose graph has vertex at the point (2,5).

 

Which of the following statements are true

 

a. x=4 is in the domain of f

b. y=1 is in the range of f

c. y=7 is in the range of f

d. f is a one to one function

e. 2 is the maximum value of f

f. 5 is the minimum value of f

Answer 1

The equation of a parabola can be written as y = a(x - h)² + k, where (h, k) is the vertex. If a > 0, then the parabola opens upward, which means that the vertex would represent the minimum point on the graph of the parabola. A parabola that opens upward cannot be one to one because it fails the horizontal line test. In other words, because a horizontal line will intersect the graph in more than one point, then the function is not one to one.