Question

The function f (x) is given as the equation f (x) = -x2 6x 11. Some points of the function g (x) are given in the table below. X y=g(x) 5 -27 4 -12 3 -1 NW 2 6 1 9 0 8 -1 3 -2 -6 -3 -19 -4 -36 -5 -57 Which of the quadratic functions has the larger maximum? Explain your reasoning.

Answer 1

To determine which quadratic function has the larger maximum, we compare the maximum points of the two functions. The maximum point of f(x) = -x^2 + 6x + 11 is (3, 20), while the maximum point of y = x^2 is (0, 0). Therefore, f(x) has the larger maximum point.

Step-by-step explanation:

To determine which quadratic function has the larger maximum, we need to compare the values of the maximum points of the two functions. The function f(x) = -x^2 + 6x + 11 is given. The maximum point of a quadratic function occurs at the vertex, which is given by the formula x = -b/2a. For f(x), a = -1, b = 6, and c = 11.

Plugging these values into the formula, we get x = -6/(2*(-1)) = 3.

Now we can substitute this value of x into f(x) to find the maximum point.

f(3) = -(3)^2 + 6(3) + 11

f(3) = -9 + 18 + 11

f(3) = 20

Therefore, the maximum point of f(x) is (3, 20). Next, we need to compare this to the maximum point of the other quadratic function y = x^2. Since y = x^2 is an upward-opening parabola, the maximum point occurs at the vertex, which is the point (0, 0). Since the y-coordinate of the maximum point for f(x) is greater than the y-coordinate of the maximum point for y = x^2, we can conclude that f(x) = -x^2 + 6x + 11 has the larger maximum.