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The functions 
f(x)=-(x-4)^(2)+3 and 
g(x)=-(x-4)^(2)+5 are graphed in the same 
xy-plane as 
y=f(x) and 
y=g(x). If 
(h_(1),k_(1)) is the vertex of the graph of function 
f and 
(h_(2),k_(2)) is the vertex of the graph of function 
g, then what is 
k_(2)-k_(1) ?
Choose 1 answer:
(A) -2
(B) 0
(C) 2
(D) 8

The functions f(x)=(x4)2+3f(x) = -(x-4)^{2} + 3 and g(x)=(x4)2+5g(x) = -(x-4)^{2} + 5 are graphed in the same xyxy-plane as y=f(x)y = f(x) and y=g(x)y = g(x). If (h1,k1)(h_{1}, k_{1}) is the vertex of the graph of function ff and (h2,k2)(h_{2}, k_{2}) is the vertex of the graph of function gg, then what is k2k1k_{2} - k_{1}?\newlineChoose 11 answer:\newline(A) 2-2\newline(B) 00\newline(C) 22\newline(D) 88

Full solution

Q. The functions f(x)=(x4)2+3f(x) = -(x-4)^{2} + 3 and g(x)=(x4)2+5g(x) = -(x-4)^{2} + 5 are graphed in the same xyxy-plane as y=f(x)y = f(x) and y=g(x)y = g(x). If (h1,k1)(h_{1}, k_{1}) is the vertex of the graph of function ff and (h2,k2)(h_{2}, k_{2}) is the vertex of the graph of function gg, then what is k2k1k_{2} - k_{1}?\newlineChoose 11 answer:\newline(A) 2-2\newline(B) 00\newline(C) 22\newline(D) 88
  1. Identify Vertex of f(x)f(x): Identify the vertex of the graph of function f(x)f(x). The vertex form of a quadratic function is given by a(xh)2+ka(x - h)^2 + k, where (h,k)(h, k) is the vertex of the parabola. For f(x)=(x4)2+3f(x) = -(x - 4)^2 + 3, the vertex (h1,k1)(h_1, k_1) is (4,3)(4, 3).
  2. Identify Vertex of g(x)g(x): Identify the vertex of the graph of function g(x)g(x). The vertex form of a quadratic function is given by a(xh)2+ka(x - h)^2 + k, where (h,k)(h, k) is the vertex of the parabola. For g(x)=(x4)2+5g(x) = -(x - 4)^2 + 5, the vertex (h2,k2)(h_2, k_2) is (4,5)(4, 5).
  3. Calculate Difference in k: Calculate the difference between k2k_2 and k1k_1.k2k1=53=2k_2 - k_1 = 5 - 3 = 2.

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