SOLUTION: Find the x- and y-intercepts. If no x-intercepts exist, state so. f(x) = -x^2 + 7x - 18 A) No x-intercepts, (0, 18) B) No x-intercepts, (0, -18) C) ((-x(+ or -)sqrt 121)/(

Question 201548: Find the x- and y-intercepts. If no x-intercepts exist, state so.
f(x) = -x^2 + 7x - 18
A) No x-intercepts, (0, 18)
B) No x-intercepts, (0, -18)
C) ((-x(+ or -)sqrt 121)/(2),0) , (0, -18)
D) ((-x(+ or -)sqrt 121)/(2),0) , (0, 18)

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
We'll start with the y-intercept since it is easier. The y-intercept occurs when x=0. (Think about it. All the points along the y-axis have an x-coordinate that is 0.) So to find the y-intercept find the point where x=0, In other words find f(0).
which simplifies to:

So the y-intercept is (0, 18).

Similarly to find x-intercepts we find we y=0:

Since this will not factor, we will try the quadratic formula: . To use this formula we need the values of a, b and c. Since the general form is:
we will need to rewrite our equation with additions:

From this we can see that
a = -1
b = 7
c = -18
Substituting these values into the quadratic formula we get:

Simplifying:

At this point we can go no farther. When we square any Real number we either get zero or a positive number, never a negative. So it is impossible to square a Real number and get -23. In other words does not exist among the Real numbers. This means that there are no x-intercepts on our graph.
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