How to isolate x in a quadratic equation

It's a parabola that opens downward and has roots of 0 and 3.In summary, the conversation discusses isolating x in a quadratic equation and using the quadratic formula to solve for x. The possibility of two solutions for x and using the graph to visualize the equation is also mentioned.
  • #1
f24u7
46
0

Homework Statement





I just would like to know how would I isolate x in a quadratic equation such as y = x(3-x).



Homework Equations



quadratic equation.



The Attempt at a Solution




I don't think you can use completing square in this, and quadratic equation doesn't really help much since I'm not solving for x.





Thanks in advance
 
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  • #2
Assuming you're going to input values of x to find y, I think you can use the quadratic equation to get x as a function of y, and then use some algebra to create y as a function of x. The only problem would be you would get two answers for x as a function of y, so bouth would need to be considered. Try letting y be an arbitrary value and use the quadratic equation on this:
[tex]
-x^2+3x-y=0
[/tex]
 
  • #3
Why couldn't you complete the square? Just multiply both sides by negative one, so you have
[itex]-y=x^2-3x [/itex], then go from there.
 
  • #4
f24u7 said:

Homework Statement





I just would like to know how would I isolate x in a quadratic equation such as y = x(3-x).



Homework Equations



quadratic equation.



The Attempt at a Solution




I don't think you can use completing square in this, and quadratic equation doesn't really help much since I'm not solving for x.
On the contrary, you are solving for x! To solve an equation for x means to write it as x= ... where there is no "x" on the right. And that is exactly what you mean by "isolating x".

[itex]y= x(3- x)= 3x- x^2[/itex] so that [itex]x^2- 3x+ y= 0[/itex]. Use the quadratic formula,
[tex]\frac{-b\pm\sqrt{b^2- 4ac}}{2a}[/tex]
with a= 1, b= -3 and c= y. The fact that c is "y" rather than a specific number just means that your solution will depend upon y.





Thanks in advance
 
  • #5
Have you tried drawing the graph?
 

FAQ: How to isolate x in a quadratic equation

1. How do I isolate x in a quadratic equation with a coefficient on the x^2 term?

To isolate x in a quadratic equation with a coefficient on the x^2 term, you need to use the quadratic formula or complete the square. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the x^2, x, and constant terms, respectively. Completing the square involves rewriting the equation in the form (x + p)^2 = q and then solving for x using inverse operations.

2. Can I isolate x in a quadratic equation without using the quadratic formula or completing the square?

Yes, there are various other methods you can use to isolate x in a quadratic equation, such as factoring, graphing, or using the quadratic equation solver on a calculator. However, some equations may require the use of the quadratic formula or completing the square to isolate x.

3. What do I do if there is no constant term in the quadratic equation?

If there is no constant term in the quadratic equation, you can still isolate x by factoring out the greatest common factor (GCF) from the x^2 and x terms. Once the GCF is factored out, you can proceed to solve for x using inverse operations.

4. Can I isolate x in a quadratic equation with imaginary solutions?

Yes, you can isolate x in a quadratic equation with imaginary solutions. The quadratic formula can still be used, and the result will have imaginary solutions if the discriminant (b^2 - 4ac) is negative. Remember to simplify any imaginary numbers in the solution, such as √(-1) being equal to i.

5. Is it possible to have more than one solution when isolating x in a quadratic equation?

Yes, it is possible to have more than one solution when isolating x in a quadratic equation. This is because a quadratic equation can have two solutions, also known as roots, when graphed on a coordinate plane. However, there are also cases when a quadratic equation has only one solution or no real solutions at all.

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