How would you go about solving this? Im totally confused. Thanks!
Find the value of k such that the graph of f contains the given point. Write k as a simplified fraction if it is not a whole number.
f(x) = kx^3 - 3x^2 + kx + 3; (-1, 8)
Y = K(-1)^3-3(-1)^2+K(-1)+3 = 8,
-K-3-K+3 = 8,
-2K = 8,
K = -4.
To find the value of k such that the graph of f contains the point (-1, 8), we need to substitute the x and y coordinates of the point into the equation for f(x) and solve for k.
1. Start with the equation for f(x):
f(x) = kx^3 - 3x^2 + kx + 3
2. Substitute the x and y coordinates from the given point (-1, 8) into the equation:
f(-1) = k(-1)^3 - 3(-1)^2 + k(-1) + 3
3. Simplify the equation:
f(-1) = k(-1) - 3 + (-k) + 3
f(-1) = -k - 3 - k + 3
f(-1) = -2k
4. The y-coordinate of the given point is 8, so we have:
8 = -2k
5. Solve for k:
Divide both sides of the equation by -2:
8 / -2 = -2k / -2
-4 = k
Therefore, the value of k that makes the graph of f contain the point (-1, 8) is -4.