SOLUTION: Find the x- and y-intercepts. If no x-intercepts exist, state so f(x) = x2 - 6x + 17 (Points: 3) a No x-intercepts, (0, 17) b No x-intercepts, (0, -17) c (

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the x- and y-intercepts. If no x-intercepts exist, state so f(x) = x2 - 6x + 17 (Points: 3) a No x-intercepts, (0, 17) b No x-intercepts, (0, -17) c (      Log On


   

Question 233414: Find the x- and y-intercepts. If no x-intercepts exist, state so
f(x) = x2 - 6x + 17 (Points: 3)
a No x-intercepts, (0, 17)
b No x-intercepts, (0, -17)
c (6√104)/2 (0, -17)
d (6√104)/2, (0, 17)

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x2 - 6x + 17
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B17+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-6%29%5E2-4%2A1%2A17=-32.

The discriminant -32 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -32 is + or - sqrt%28+32%29+=+5.65685424949238.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B17+%29

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The y-intercept is f(0) = 17
There are no x-intercepts.