The graph of f(x) = -x2 - 2x + 8 is shown. Which of the following describes all solutions for f(x)? O(x -x2 - 2x + 8) for all real numbers
O(-4,0), (-1,9), (0, 8), (2.0)
O(-4.0), (2,0)
O(x, y) for all real numbers

y-intercept is when x = 0:

So the y-intercept is (0, 8)

x-intercepts are when f(x) = 0:

Therefore:

So the x-intercepts are (-4, 0) and (2, 0)

The vertex is the turning point of the parabola.  The x-value of the vertex is the x-value between the 2 zeros (x-intercepts).

Therefore, the x-value of the vertex is

Substituting x = -1 into the function:

So the vertex is (-1, 9)

The domain is the input values, so x = all real numbers.

The range is the output values, so the range is

Therefore, (-4, 0), (-1, 9), (0, 8) and (2, 0) are solutions of the function, HOWEVER they are not ALL the solutions.

All solutions of the function are:

for all real numbers of x

ok then what happened.