The quadratic function f(x) = x^2 is transformed to g(x) = -2/3(x+3)^2 + 6 The point (6,36) on the graph of f is transformed to which point on the graph of g?
Could someone please show me how to solve this:\
shift x left 3 (reduce x by three, since g(x+3) = f(x))
scale y by -2/3
shift y up by 6
(3,36*(-2/3)+6) = (3,-24+6) = (3,-18)
check:
g(3) = -2/3 * (3+3)^2 + 6 = -18
To find the point on the graph of g(x) that corresponds to the point (6, 36) on the graph of f(x), we need to substitute x = 6 into g(x) and find the corresponding y-value.
Given that g(x) = -2/3(x + 3)^2 + 6, we substitute x = 6 into g(x):
g(6) = -2/3(6 + 3)^2 + 6
First, we simplify the expression inside the parentheses:
g(6) = -2/3(9)^2 + 6
Next, we square 9:
g(6) = -2/3(81) + 6
Now, we multiply -2/3 by 81:
g(6) = -54 + 6
Finally, we add -54 and 6 to get the value of g(6):
g(6) = -48
Therefore, the point (6, 36) on the graph of f(x) is transformed to the point (-48) on the graph of g(x).
To solve this problem, we need to find the corresponding point for the transformation of the given point (6, 36) on the graph of the quadratic function f(x) = x^2 to the new quadratic function g(x) = -2/3(x+3)^2 + 6.
Step 1: Start by substituting the x-coordinate of the given point, 6, into the transformed function g(x).
g(x) = -2/3(x+3)^2 + 6
g(6) = -2/3(6+3)^2 + 6
g(6) = -2/3(9)^2 + 6
g(6) = -2/3(81) + 6
Step 2: Simplify the expression.
g(6) = -2/3(81) + 6
g(6) = -2/3 * 81/1 + 6
g(6) = -2 * 81/3 + 6
g(6) = -162/3 + 6
g(6) = -54 + 6
g(6) = -48
Therefore, the corresponding point on the graph of g(x) for the point (6, 36) on the graph of f(x) is (-48, 36).