Question

(a) Determine the value of "k" in the function f(x) = kx^2 - 3x if it passes through the point (2, 60).

(b) State the x-intercept(s) and y-intercept(s) of the function.
(c) Sketch a graph of the function, including x-intercept(s), y-intercept(s), behavior around x-intercept(s), and end behavior.

Answer 1

From the graph we have that

x-intercept = (0, 0) and (0.18, 0)

y-intercept( = (0, 0)

The end behavior of the graph is

x → -∞, y → ∞ and x → ∞, y → ∞

How to find the value of k

Since the graph passed through the point (2, 60) we solve for k by substituting as below

kx² - 3x = y

k(2)² - 3(2) = 60

4k = 60 + 6

k = 66/4

k = 16.5

The full equation used for the graph is 16.5x² - 3x