For questions 33 34 let fx 2x2 7x 7 33 What is the domain an

For questions 33 34, let f(x) 2x2 7x 7 33. What is the domain and range of f(x)? 34. At what point is the vertex of fX) located? Is it a maximum or a minimum? Justify.

Solution

f(x)= 2x²-7x+7

Vertex,x=-b/2a = -(-7)/4=7/4=1.75

f(1.75)= 2(1.75)²-7(1.75)+7 = .875

Vertex= (1.75,.875)

33. domain

Here there is no restriction on x. Therefore domain is (-infinity,infinity)

Range

The y values should be greater than or equal to .875

Therefore range is [.875,infinity)

34. Vertex= (1.75,.875)

Here a is 2 which is greater than 0. In that case the vertex is minimum.