1. Where is the point symmetric to the y-intercept of the function f(x)=−x^2 +5x−6

A. (5/2,-6)
B. (-5,-6)
C. (5,-6)
D. (-5/2,-6)

1 answer

To find the point symmetric to the y-intercept, we need to find the y-coordinate of the y-intercept first.

The y-intercept is the point where the graph of the function intersects the y-axis. It occurs when x = 0.

So, plugging in x = 0 into the equation f(x) = -x^2 + 5x - 6, we get:

f(0) = -(0)^2 + 5(0) - 6 = -6

Therefore, the y-intercept is (0, -6).

To find the point symmetric to the y-intercept, we need to find the x-coordinate first. The x-coordinate of the point symmetric to the y-intercept is the same as the x-coordinate of the y-intercept, but with the opposite sign.

So, the x-coordinate of the point symmetric to the y-intercept is 0.

Now, to find the y-coordinate, we need to evaluate the function for x = 0.

f(0) = -0^2 + 5(0) - 6 = -6

Therefore, the point symmetric to the y-intercept is (0, -6).

None of the given answer choices matches the point (0, -6), so the correct answer cannot be determined from the given choices.