Help Solving (y - a)^2 = p(x - e) Problem - Nicole

Thread starter lilcoley23@ho
Start date Jan 1, 2010

In summary, to solve the equation (y - a)^2 = p(x - e), you will need to use the FOIL method to expand the equation and then isolate the variable by using the inverse operations of addition and multiplication. If there are constants on both sides, they can be combined to one side before isolating the variable. To check the solution, you can substitute the values into the original equation. Special cases to consider include p = 0, y = a and x = e, and p < 0.

Jan 1, 2010

lilcoley23@ho

I'm looking at an example of a problem in my book and one line says

(y - a)^2 = p(x - e)

and then it says by subtracting they get

2ay - a^2 = pe

I'm not seeing what they subtracted to get that...

Please help me!

Nicole

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Jan 1, 2010

lilcoley23@ho

Nevermind, I figured it out...I was actually subtracting out an equation from earlier in the problem.

1. What is the first step in solving the equation (y - a)^2 = p(x - e)?

The first step is to expand the equation using the FOIL method, which stands for First, Outer, Inner, and Last. This means multiplying the first terms, outer terms, inner terms, and last terms of the binomials.

2. How do I isolate the variable in (y - a)^2 = p(x - e)?

To isolate the variable, you will need to use the inverse operations of addition and multiplication. First, distribute the p to the terms inside the parentheses. Then, subtract the constant term on the right side from both sides. Finally, take the square root of both sides to isolate the variable.

3. What do I do if there is a constant on both sides of the equation (y - a)^2 = p(x - e)?

In this case, you will need to combine the constant terms on one side of the equation. For example, if there is a constant term of 5 on both sides, you can subtract 5 from both sides to eliminate it. Then, follow the steps for isolating the variable as normal.

4. How do I check if my solution for (y - a)^2 = p(x - e) is correct?

To check if your solution is correct, you can substitute the values of the variables into the original equation and see if it satisfies the equation. For example, if your solution is y = 3 and x = 2, you would substitute those values into the equation to see if (3 - a)^2 = p(2 - e) is true.

5. Are there any special cases to consider when solving (y - a)^2 = p(x - e)?

Yes, there are a few special cases to consider. First, if p = 0, the equation becomes (y - a)^2 = 0, and the only solution is y = a. Second, if y = a and x = e, the equation becomes 0 = 0, and there are infinitely many solutions. Lastly, if p < 0, there are no real solutions to the equation.