Solve f(x) + G(x) + H(x): x^2 + 5x + 1

  • Thread starter sfeld
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In summary, to solve the given equation, which involves adding three functions to a quadratic function, one can use algebraic methods such as factoring or the quadratic formula. A graphing calculator can also be used to find the solutions visually. The coefficients in the equation have specific meanings, representing the curvature, shift, and y-intercept of the parabola. The solutions can be used in other calculations and have various real-world applications in fields such as physics, economics, and biology.
  • #1
sfeld
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f(x) = 2x - 1; G(x) = 3x + 2; H(x) = x^2

Find f(x) + G(x) + H(x)

Answer is x^2 + 5x + 1.
can someone explain the problem to me please <3


////////////Oh I see now, I was putting the wrong sign in that's why I was'nt getting it, my carless mistakes D:! please forgive D:
 
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  • #2
f(x) + G(x) + H(x) = (2x - 1) + G(x) + H(x).

Can you take it from there?
 
  • #3


No worries! Let's break down the problem. The given equation is f(x) + G(x) + H(x) = x^2 + 5x + 1. This means that we need to combine the functions f(x), G(x), and H(x) to get the final result of x^2 + 5x + 1.

First, let's substitute the given values for f(x), G(x), and H(x) into the equation: (2x-1) + (3x+2) + (x^2) = x^2 + 5x + 1. Now we can simplify the equation by combining like terms. We have 2x + 3x + x^2 - 1 + 2 = x^2 + 5x + 1. This gives us a simplified equation of x^2 + 5x + 1 = x^2 + 5x + 1. As you can see, the final result is the same as the given equation, which means that our answer is correct!

I hope this explanation helps. Remember to always double check your signs and terms when solving equations. Keep practicing and you'll get the hang of it!
 

1. How do I solve this equation?

This equation involves adding three different functions, f(x), g(x), and h(x), to a quadratic function, x^2 + 5x + 1. To solve, first combine like terms and then use algebraic methods, such as factoring or the quadratic formula, to find the values of x that make the equation true.

2. Can I use a graphing calculator to solve this equation?

Yes, a graphing calculator can be a helpful tool to visually see the solutions to this equation. You can also use the "zero" or "root" function to find the x-intercepts or solutions of the equation.

3. What is the significance of the coefficients in this equation?

The coefficient of x^2, which is 1 in this equation, represents the steepness or curvature of the parabola. The coefficient of x, which is 5 in this equation, represents the direction and magnitude of the shift of the parabola on the x-axis. The constant term, which is 1 in this equation, represents the y-intercept or where the parabola crosses the y-axis.

4. Can I use the solutions to this equation in other calculations or applications?

Yes, the solutions to this equation represent the x-values where the equation is true. These values can be used in other calculations or applications, such as finding the roots of a polynomial function or determining the maximum or minimum value of a quadratic function.

5. How does this equation relate to real-world problems or scenarios?

This equation can represent a variety of real-world problems or scenarios, such as finding the maximum height of a projectile, determining the optimal production level for a business, or predicting the growth of a population over time. It is a useful tool for modeling and solving problems in fields such as physics, economics, and biology.

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