F(x) = x ^ 2 - 8x + 7 Do the minima of the two functions have the same x-value?
Which of the functions has the greater minimum?

They have the same x-value
f(x) has the greater minimum
Step-by-step explanation:
To find the vertex of a second degree equation, in this case the minimum value, we can use the following equation:
x = -b / 2a
Remember that a second degree equation has the following form:
ax^2 + bx + c
so a = 1, b = -8 and c = 7. Now you have to substitute in the previous equation
x = - (-8) / 2(1)
x = 8 / 2
x = 4
This means that the two functions have the same x-value.
The y value of f(x) would be
f(4) = (4)^2 - 8(4) + 7
f(4) = 16 - 32 + 7
f(4) = -9
So the vertex, or minimun value of f(x) would be at the point (4, -9).
The vertex, or minimun value of g(x) is at the point (4, -4).
So f(x) has a minimum value of -9 and g(x) a minimum value of -4.