SOLUTION: given f(x) = ax^2 + bx + 5. Find a and b such that f(x + 1) - f(x) = 8x + 3

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: given f(x) = ax^2 + bx + 5. Find a and b such that f(x + 1) - f(x) = 8x + 3      Log On


   

Question 212341: given f(x) = ax^2 + bx + 5. Find a and b such that f(x + 1) - f(x) = 8x + 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since f%28x%29=ax%5E2+%2B+bx+%2B+5, this means that .


Or simply f%28x%2B1%29=ax%5E2%2B%282a%2Bb%29x%2B%28a%2Bb%2B5%29


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f%28x+%2B+1%29+-+f%28x%29+=+8x+%2B+3 Start with the given equation.


%28ax%5E2%2B%282a%2Bb%29x%2B%28a%2Bb%2B5%29%29+-+%28ax%5E2+%2B+bx+%2B+5%29+=+8x+%2B+3 Plug in f%28x%2B1%29=ax%5E2%2B%282a%2Bb%29x%2B%28a%2Bb%2B5%29 and f%28x%29=ax%5E2+%2B+bx+%2B+5


ax%5E2%2B%282a%2Bb%29x%2B%28a%2Bb%2B5%29+-+ax%5E2+-+bx+-+5+=+8x+%2B+3 Distribute


2ax%2B%28a%2Bb%29+=+8x+%2B+3 Combine like terms.


So we then get that 2ax=8x which means 2a=8 or a=4

Also, we find that a%2Bb=3. Plug in a=4 to get 4%2Bb=3 and solve to get b=-1