Question

For the function f(x) = 0.25x^2 - 8x + 600, what is the x-value of the vertex?

A. 8
B. -8
C. 16
D. -16

For the same function, f(x) = 0.05x^2 - 7x + 300, identify A, B, and C:
A. 0.05, -7, 300
B. 0.05, 7, -300
C. 0.25, -8, 600
D. 0.25, 8, -600

Answer 1

The x-value of the vertex for the function f(x) = 0.25x^2 - 8x + 600 is found using the vertex formula and is 16, making option C correct. For the function f(x) = 0.05x^2 - 7x + 300, A, B, and C are the coefficients of x^2, x, and the constant term respectively, making option A correct.

Step-by-step explanation:

To find the x-value of the vertex for the quadratic function f(x) = 0.25x^2 - 8x + 600, we can use the formula -b/(2a), where a is the coefficient of x^2 and b is the coefficient of x. In this case, a = 0.25 and b = -8, so the x-value of the vertex is:

x = -(-8) / (2 * 0.25)

x = 8 / 0.5

x = 16

Thus, the correct answer is C. 16.

For the quadratic function f(x) = 0.05x^2 - 7x + 300, the coefficients corresponding to A, B, and C are directly taken from the function as the coefficients of x^2, x, and the constant term respectively. Therefore, the values are:

A = 0.05, B = -7, C = 300

The correct answer for this part is A. 0.05, -7, 300.