Final answer:
The x-intercepts of the equation Y = −3(x−5)(x−4) are the points where the graph crosses the x-axis. By setting Y to 0 and solving for x, the x-intercepts are found to be (5, 0) and (4, 0), which corresponds to answer option (a).
Step-by-step explanation:
To find the x-intercepts of the equation Y = −3(x−5)(x−4), we need to set the equation equal to 0 and solve for x. An x-intercept is a point where the graph of the equation crosses the x-axis, which occurs when Y is 0.
So, we set the equation to 0:
0 = -3(x-5)(x-4)
Since the equation is already factored, we can easily find the x-intercepts by setting each factor equal to 0:
(x-5) = 0 and (x-4) = 0
To find the x-intercepts of the equation Y = −3(x−5)(x−4), we set Y to zero and solve for x.
0 = −3(x−5)(x−4)
This equation will be true if either (x-5) or (x-4) equals zero.
To find the x-intercepts, we solve for x:
x-5 = 0 => x = 5
x-4 = 0 => x = 4
Therefore, the x-intercepts of the equation are (5, 0) and (4, 0).
Solving these, we get the solutions x = 5 and x = 4, which means that the x-intercepts are (5, 0) and (4, 0). Hence, the correct answer is (a) (5, 0) and (4, 0).