The coordinates of the vertex are (9 , -20)
The axis of symmetry is a vertical line at x = 9
The maximum value is -20 occurs at x = 9
The domain of the function is {x : x ∈ R}
The range of the function is {y : y ≤ -20}
Step-by-step explanation:
The quadratic function in the vertex form is f(x) = a(x - h)² + k, where
1. (h , k) are the coordinates of its vertex
2. If a > 0, then the function has minimum value
If a < 0, then the function has maximum value
3. The minimum value or the maximum value is y = k occurs at x = h
4. The axis of symmetry is a vertical line passes through the vertex
at x = h
5. The domain of the function is {x : x ∈ R} , where R is the set of the
real numbers
6. The range of the function is y ≥ k if it is minimum ⇒ {y : y ≥ k}
The range of the function is y ≤ k if it is maximum ⇒ {y : y ≤ k}
∵ f(x) = -(x - 9)² - 20
∴ a = -1
∴ h = 9
∴ k = -20
∵ (h , k) are the coordinates of the vertex of f(x)
∴ The coordinates of the vertex are (9 , -20)
∵ The axis of symmetry is a vertical line passes through the vertex at
x = h
∵ h = 9
∴ The axis of symmetry is a vertical line at x = 9
∵ a = -1
∵ -1 < 0
∴ The vertex is a maximum point
∵ The maximum value of f(x) = k occurs at x = h
∵ k = -20 and h = 9
∴ The maximum value is -20 occurs at x = 9
∵ The domain of the function is all real numbers
∴ The domain of the function is {x : x ∈ R}
∵ The range of the function is y ≤ k
∵ k= -20
∴ The range of the function is {y : y ≤ -20}
The coordinates of the vertex are (9 , -20)
The axis of symmetry is a vertical line at x = 9
The maximum value is -20 occurs at x = 9
The domain of the function is {x : x ∈ R}
The range of the function is {y : y ≤ -20}
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