SOLUTION: Find the inverse of quadratic function, graph function and its inverse in the same coordinate plane. y=x^2-2x+1 How do I find the answer?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the inverse of quadratic function, graph function and its inverse in the same coordinate plane. y=x^2-2x+1 How do I find the answer?      Log On


   

Question 202334: Find the inverse of quadratic function, graph function and its inverse in the same coordinate plane.
y=x^2-2x+1
How do I find the answer?
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the inverse of quadratic function, graph function and its inverse in the same coordinate plane.
y=x^2-2x+1
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Interchange x and y to get:
x = y^2 - 2y + 1
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Solve for "y":
y^2 - 2y + (1-x) = 0
----------------
Use the quadratic formula to solve for "y":
y = [2 +- sqrt(4 - 4(1-x)]/2
y = [2 +- sqrt(4(1-(1-x)[/2
y = [2 + 2sqrt(x)]/2 or y = [2 - 2sqrt(x)]/2
y = [1 + sqrt(x)] or y = [1-sqrt(x)]
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Graph:

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Cheers,
Stan H.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
To find the inverse of the function:
y+=+x%5E2-2x%2B1 Exchange the x- and y-variables, then solve the resulting equation for y, thus:
x+=+y%5E2-2y%2B1 Solve this equation for y. Subtract X from both sides.
y%5E2-2y%2B%281-x%29+=+0 Use the quadratic formula to solve.
y+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a In the equation just developed, a = 1, b = -2, and c = (1-x).
y+=+%28-%28-2%2B-sqrt%28-2%29%5E2-4%281%29%281-x%29%29%29%2F2%281%29 Simplify.
y+=+%282%2B-sqrt%284-4%2B4x%29%29%2F2
y+=+%282%2F2%29%2Bsqrt%284x%29%2F2 or y+=+%282%2F2%29-sqrt%284x%29%2F2 which can be further simplified into:
highlight%28y%5E-1+=+1%2B-sqrt%28x%29%29 This is the inverse.
In order to graph this, you must graph the two solutions as separate graphs:
y+=+1%2Bsqrt%28x%29 and y+=+1-sqrt%28x%29
The graph looks like:
graph%28400%2C400%2C-5%2C10%2C-5%2C10%2Cx%5E2-2x%2B1%2C1%2Bsqrt%28x%29%2C1-sqrt%28x%29%29
The red parabola is the graph of the given quadratic equation while the blue & green graphs combine to form the graph of the inverse funtion.