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

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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)   (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
Answer by Alan3354(69443)   (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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=5 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.61803398874989, -0.618033988749895. Here's your graph:

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