what value represents the vertical translation from the graph of the parent function $f(x)=x^{2}$ to the…
what value represents the vertical translation from the graph of the parent function $f(x)=x^{2}$ to the graph of the function $g(x)=(x + 5)^{2}+3$?\n-5\n-3\n3\n5
Answer
Explanation:
Step1: Recall the vertex form of a parabola
The vertex form of a parabola is (y = a(x - h)^2 + k), where ((h,k)) is the vertex of the parabola. For the parent function (f(x)=x^{2}), the vertex is ((0,0)). For the function (g(x)=(x + 5)^{2}+3=(x-(-5))^{2}+3), the vertex is ((-5,3)).
Step2: Identify the vertical translation
The vertical translation of a function (y = f(x)) to (y=f(x)+k) is given by the value of (k). In the transformation from (f(x)=x^{2}) (vertex ((0,0))) to (g(x)=(x + 5)^{2}+3) (vertex ((-5,3))), the vertical change is from (y = 0) to (y=3). The formula for vertical translation is (y=f(x)+k), where (k) is the amount of vertical shift. Here, (k = 3).
Answer:
3