Compare each function to f, shown in the table. Which function has lesser minimum value? Explain


h(x) = x² + x – 3.5

The correct answer is: -3.75

We have given two functions f(x) and h(x).
h(x) = x² + x – 3.5
For f(x) , minimum value of the function will be the y-coordinate of the given point which has minimum values
(1,0) , (2,-3) , (3,-4) , (4,-3) (5,0)
In the given points minimum value of is (3,-4)
So, the ,minimum value of f(x) is -4.
In h(x) = x² + x – 3.5,  a= 1, b= 1, and c = -3.5. So, the equation for the axis of symmetry is given by

x = −(1)/2(1)

x = -1/2

x = -0.5
The equation of the axis of symmetry for h(x) = x² + x – 3.5 is x = -0.5.
The x coordinate of the vertex is the same:

h =-0.5
The y coordinate of the vertex is :

k = f(h)

k = h² + h – 3.5

k = (-0.5)² + (-0.5) – 3.5

k = 0.25 – 0.5 – 3.5

k = -3.75
Therefore, the vertex is (-0.5 , -3.75)
The minimum value of g(x) will be the y-coordinate of vertex = -3.75