Let f(x)=x^2−10x−11 . enter the x-intercepts of the quadratic function in the boxes.

ANSWER

The y-intercept is (0,-11)

The x-intercepts are:

(-1,0) and (11,0)

EXPLANATION

The given function is

To find the y-intercept, we put x=0 into the function.

The y-intercept is (0,-11)

To find the x-intercepts, we put f(x)=0.

This implies that,

The x-intercepts are:

(-1,0) and (11,0)

there are no short passages to look at

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.