Question

Give the domain and range of the quadratic function whose graph is described.

Maximum = -8 at x=5
The domain of the function is (Type your answer in interval notation.)
a) [infinity],5
b) 5,[infinity]
c)[infinity]-8]
d)-8, [infinity]

Answer 1

a) The domain of the function is (-∞, 5].

Step-by-step explanation:

The given information indicates that the quadratic function has a maximum value of -8 at x = 5. In a quadratic function written in the form f(x) = ax² + bx + c, the vertex form is f(x) = a(x - h)² + k, where (h, k) is the coordinates of the vertex. In this case, since the maximum occurs at x = 5, the vertex form is f(x) = a(x - 5)² - 8.

For a quadratic function, the domain is the set of all real numbers, denoted as (-∞, ∞). The range, in this case, is (-8, ∞) since the vertex is the maximum point, and the parabola opens downwards.

Therefore, the correct answer is (a) (-∞, 5] for the domain. The interval notation (-∞, 5] signifies that the function is defined for all real numbers less than or equal to 5.

In summary, understanding the properties of the vertex form of a quadratic function allows us to determine the domain and range based on the given information about the maximum point and its location on the graph. OPTION A