Given the function f(x) = 5x^2 - 40x + 87 and the quadratic function g(x) represented in the table below, which function has the smaller minimum value?

Question

x =
1 2 3 4 5
g(x) =
34 19 10 7 10

Answer 1

To find the minimum value of the quadratic function g(x) represented in the table, we need to find the lowest value of g(x) in the table.

The minimum value of g(x) in the table is 7 when x = 4.

Now let's find the minimum value of the function f(x) = 5x^2 - 40x + 87.

The minimum value of a quadratic function of the form f(x) = ax^2 + bx + c occurs at x = -b/2a.

For the function f(x) = 5x^2 - 40x + 87, a = 5 and b = -40.

x = -(-40) / 2(5)
x = 40 / 10
x = 4

Therefore, the minimum value of the function f(x) = 5x^2 - 40x + 87 occurs when x = 4.

Plugging x = 4 into the function:

f(4) = 5(4)^2 - 40(4) + 87
f(4) = 5(16) - 160 + 87
f(4) = 80 - 160 + 87
f(4) = 167 - 160
f(4) = 7

Therefore, the minimum value of the function f(x) = 5x^2 - 40x + 87 is 7 when x = 4.

Comparing the minimum values:
- The minimum value of g(x) is 7.
- The minimum value of f(x) is also 7.

Both functions have the same minimum value of 7.