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)
To find the point symmetric to the y-intercept of the function f(x) = −x^2 + 5x − 6, we first need to find the y-intercept.
The y-intercept occurs when x = 0. So we substitute x = 0 into the function:
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 reflect the y-intercept across the y-axis. Since we are reflecting across the y-axis, the x-coordinate remains the same but the sign changes.
So the point symmetric to the y-intercept is (-0, -6), which simplifies to (0, -6).
Therefore, the correct answer is C. (5, -6).
To find the point symmetric to the y-intercept, we first need to determine the y-intercept of the function f(x) = -x^2 + 5x - 6. The y-intercept occurs when x is equal to 0.
So, let's substitute x = 0 into the function:
f(0) = -(0)^2 + 5(0) - 6
f(0) = -0 + 0 - 6
f(0) = -6
Therefore, the y-intercept is (0, -6).
To find the point symmetric to the y-intercept, we need to consider that the y-coordinate remains the same, but the x-coordinate is the opposite sign. In this case, the x-coordinate is 0, so its opposite sign is also 0.
So, the point symmetric to the y-intercept is (0, -6).
However, none of the answer choices provided match this point.
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.