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Problem: A non-linear system consists of two functions: f(x) = x^2 + 2x + 1 and g(x) = 3 - x - x^2. 

A. Solve the system algebraically. (Hint: set the two functions equal to each other and solve the resulting function.) You should obtain a quadratic equation. Solve it either by factoring or using the quadratic formula. Give the x-values of the solution set, then evaluate the original function to find the corresponding y-values. Give the results as ordered pairs of exact values. 

B. Make a table of values for the functions. The table may be horizontal or vertical but it must have a minimum of five x-values and the corresponding function values showing each solution, one value lower, one value higher, and one between the two solutions. indiciate the solutions by marking the x-values and the corresponding function values that are equal.

 

—- Thanks to anyone who helps!

 Apr 7, 2019
 #1
avatar+19786 
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Uhhhh....   You are given pretty explicit directions as to how to solve this.....did you try the directions?

 Apr 7, 2019
 #2
avatar+19786 
+1

 x^2 + 2x + 1 = 3 - x - x^2.

 

2x^2 + 3x -2  = 0       Factor it......or use Qudartic Formula \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)     where a = 2  b = 3   c = -2

 

(2x -1)(x +2) = 0        means x = -2  or 1/2  

      now sub these values back in to either one of the original equations to find the corresponding 'y' values........

 Apr 7, 2019

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