Determine if each of the statements about the given equation are true or false.

Question

f(x)=2x^2-16x+1

1 The parabola has a maximum

2 The Axis of Symmetry is at x = -4

3 The vertex is at (4, -31)

4 The parabola is increasing from x > 4

5 The parabola is decreasing from x > 4

Answer 1

1. False - the parabola faces up so it has a minimum
2. False - use x = -b/2a to find the x-coordinate of the vertex ( also the axis of symmetry) to get 16/4=4
3. True - from #2 we know x=4. Plug this in to get y= -31. So the vertex is ( 4, -31 )
4. True - since the parabola opens up and the axis of symmetry is x=4 it is increasing when x > 4
5. False - since the above is true this has to be false.