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)/(

Algebra ->  Equations -> 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)/(      Log On


   

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) About Me  (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).
f%280%29+=+-%280%29%5E2+%2B+7%280%29+-+18 which simplifies to:
f%280%29+=+-18
So the y-intercept is (0, 18).

Similarly to find x-intercepts we find we y=0:
0+=+-x%5E2+%2B+7x+-18
Since this will not factor, we will try the quadratic formula: x+=+%28-b+%2B-+sqrt%28b%5E2+-4ac%29%29%2F%282a%29. To use this formula we need the values of a, b and c. Since the general form is:
0+=+ax%5E2+%2B+bx+%2B+c we will need to rewrite our equation with additions:
0+=+-1%2Ax%5E2+%2B+7%2Ax+%2B+%28-18%29
From this we can see that
a = -1
b = 7
c = -18
Substituting these values into the quadratic formula we get:
x+=+%28-%287%29+%2B-+sqrt%28%287%29%5E2+-+4%28-1%29%28-18%29%29%29%2F%282%28-1%29%29
Simplifying:
x+=+%28-%287%29+%2B-+sqrt%2849+-+4%28-1%29%28-18%29%29%29%2F%282%28-1%29%29
x+=+%28-7+%2B-+sqrt%2849+-+72%29%29%2F%28-2%29
x+=+%28-7+%2B-+sqrt%28-23%29%29%2F%28-2%29
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 sqrt%28-23%29 does not exist among the Real numbers. This means that there are no x-intercepts on our graph.