Answer: the function that has the smaller minimum is g(x), and the cordinates are (0,3)
Step-by-step explanation:
We have a function for f(x) and a table for g(x)
first, quadratic functions are symmetrical.
This means that if the minimum/maximum is located at x = x0, we will have that:
f(x0 + A) = f(x0 - A)
For any real value of A.
Then when we look at the table, we can see that:
g(-1) = 7
g(0) = 3
g(1) = 7
then the minimum of g(x) must be at x = 0, and we can see that the minimum value of g(x) is 3.
Now let's analyze f(x).
When we have a quadratic equation of the shape.
y = a*x^2 + b*x + c
the minimum/maximum will be located at:
x = -b/2a
In our function we have:
a = 3
b = 6
then the minimum is at:
X = -6/2*3 = -1
f(-1) = 3*(-1)^2 + 6*-1 + 7 = 3 - 6 + 7 = 3 + 1 = 4
Then the function that has the smaller minimum is g(x), and the cordinates are (0,3)
