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

g(x) = 2x² + 8x + 3

The correct answer is: -5

Solution:- We have given two functions f(x) and g(x).
g(x) = 2x² + 8x + 3
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 g(x)= 2x² + 8x + 3,  a= 2, b= 8, and c=3. So, the equation for the axis of symmetry is given by

x = −(8)/2(2)

x = -8/4

x = -2
The equation of the axis of symmetry for g(x)= 2x² + 8x + 3 is x = -2.
The x coordinate of the vertex is the same:

h =-2
The y coordinate of the vertex is :

k = f(h)

k = 2h² + 8h + 3

k = 2(-2)² + 8(-2) + 3

k = 8 - 16 + 3

k = -5
Therefore, the vertex is (-2 , -5)
The minimum value of g(x) will be the y-coordinate of vertex = -5