Given the function f(x) = 5x^2-40x+87 and the quadratic formula g(x) represented in the table below, which function has the smaller minimum value?
x {1} {2} {3} {4} {5}
g(x) {34} {19} {10} {7} {10}
To find the minimum value of the quadratic function g(x), we look at the values in the table and find that the minimum value is 7.
Now, to compare the minimum value of g(x) with the function f(x) = 5x^2 - 40x + 87, we first need to find the minimum value of f(x). The minimum value of a quadratic function in the form f(x) = ax^2 + bx + c occurs at the vertex of the parabola, given by the formula x = -b/2a.
In this case, a = 5 and b = -40. Plugging these values into x = -b/2a, we get x = -(-40)/(2*5) = 40/10 = 4.
So, the minimum value of f(x) occurs at x = 4. Plugging x = 4 into the function f(x) = 5x^2 - 40x + 87, we get:
f(4) = 5(4)^2 - 40(4) + 87
f(4) = 80 - 160 + 87
f(4) = 7
Therefore, the function f(x) = 5x^2 - 40x + 87 has a minimum value of 7, which is the same as the minimum value of g(x).