Given that f is a quadratic function with minimum f(x)=f(3)=2, find the axis, vertex, range, and x/y intercepts.

Question

stuck on a problem and could really use some help.

Answer 1

Quadratic functions are equations of the graphs of parabolas. The minimum value of a parabola occurs at its vertex. The minimum value of this function occurs at (3, 2), so that is the vertex. The axis of symmetry will be the vertical line that passes through the vertex, which is x = 3. Since the minimum occurs at y = 2, then the range will be [2, ∞). In addition, this function does not have an x-intercept because the x-intercept occurs when y = 0. The value y = 0 does not lie in the range of this function. 

Answer 2

We could use another piece of data.

With only the minimum we need to know where another point on the parabola is,

so as to locate the image on the other side of the axis/mirror.

 

The axis is x=2 and the vertex is apparently (3,2).

 

The range is either [2,infinity] or [-infinity, 2]