SOLUTION: If f(x) = 4x + 3, evaluate f(x+h). If g(x) = x², evaluate g(x+h). If f(x) = -x + 1, evaluate f(x+h). If f(x) = -x + 1, evaluate f(x-h). Use the quadratic formula to sol

Algebra ->  Functions -> SOLUTION: If f(x) = 4x + 3, evaluate f(x+h). If g(x) = x², evaluate g(x+h). If f(x) = -x + 1, evaluate f(x+h). If f(x) = -x + 1, evaluate f(x-h). Use the quadratic formula to sol      Log On


   

Question 1000169: If f(x) = 4x + 3, evaluate f(x+h).
If g(x) = x², evaluate g(x+h).
If f(x) = -x + 1, evaluate f(x+h).
If f(x) = -x + 1, evaluate f(x-h).
Use the quadratic formula to solve the equation: x² - x - 1 = 0.
Found 2 solutions by Boreal, Alan3354:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
f(x+h)=4(x+h)+3=4x+4h+3
g(x+h)=(x+h)^2=x^2+2xh+h^2
f(x+h)=-(x+h)+1=-x-h+1
f(x-h)=-(x-h)+1=-x+h+1
x=(1/2)(1+/-sqrt(1+4)=(1/2)(1+/-sqrt(5); roots about 1.68 and -0.55
graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cx%5E2-x-1%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x² - x - 1 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B-1+=+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=%28-1%29%5E2-4%2A1%2A-1=5.

Discriminant d=5 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+5+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+5+%29%29%2F2%5C1+=+1.61803398874989
x%5B2%5D+=+%28-%28-1%29-sqrt%28+5+%29%29%2F2%5C1+=+-0.618033988749895

Quadratic expression 1x%5E2%2B-1x%2B-1 can be factored:
1x%5E2%2B-1x%2B-1+=+%28x-1.61803398874989%29%2A%28x--0.618033988749895%29
Again, the answer is: 1.61803398874989, -0.618033988749895. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-1+%29

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