SOLUTION: Determine the equation of the quadratic function With zeros of 4 + the square root of 2 and 4- Squar root of 2 that passes through the point (1,-21)

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Determine the equation of the quadratic function With zeros of 4 + the square root of 2 and 4- Squar root of 2 that passes through the point (1,-21)       Log On


   

Question 975375: Determine the equation of the quadratic function
With zeros of 4 + the square root of 2 and 4-
Squar root of 2 that passes through the point
(1,-21)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29+=+a%28x%5E%22%22-4-sqrt%282%29%5E%22%22%29%28x%5E%22%22-4%2Bsqrt%282%29%5E%22%22%29

f%28x%29+=+a%28%28x-4%29%5E2-2%5E%22%22%29
Substitute x = 1, y = f(x) = -21
-21+=+a%28%281-4%29%5E2-2%29
-21+=+a%28%28-3%29%5E2-2%29
-21+=+a%289-2%29
-21+=+a%287%29
-21+=+7a
-3=a
Substitute in
f%28x%29+=+-3%28%28x-4%29%5E2-2%5E%22%22%29
f%28x%29+=+-3%28x%5E2-8x%2B16-2%5E%22%22%29
f%28x%29+=+-3%28x%5E2-8x%2B14%5E%22%22%29
f%28x%29+=+-3x%5E2%2B24x-42%29
4%2Bsqrt%282%29=5.4, 4-sqrt%282%29=2.6, approximately
Notice that the graph of f(x) below has approximately those zeros
and it goes through (1,-21).