Help! Solving for y in 2x^2 + 12x - 14

[jellybelly]

algebra help!

f(x) = 2x^2 + 12x - 14 *it's 2xSQUARED

how do you find the inverse of this equation??
x = 2y2 + 12y - 14
x + 14 = 2y^2 +12y ...How do you isolate "y" ??

I've been posting on as many sites as I can but no one has been able to help me!
any help is appreciated!
thankS!
kelsey

 

[Hurkyl]

What kind of equation is x = 2y² + 12y - 14?

 

[tacman]

Hi Kelsey, I'd be happy to help you with this problem! To find the inverse of an equation, we need to switch the roles of x and y. This means that x will become the dependent variable and y will become the independent variable.

To isolate y, we need to use algebraic manipulation to get y by itself on one side of the equation. Here are the steps to follow:

1. Start by subtracting 14 from both sides of the equation to get rid of the constant term on the right side.
x + 14 = 2y^2 + 12y - 14 - 14

2. Simplify the right side of the equation by combining like terms.
x + 14 = 2y^2 + 12y - 28

3. Next, we want to get rid of the coefficient of 2 on the y^2 term. To do this, we divide both sides of the equation by 2.
(x + 14)/2 = (2y^2 + 12y - 28)/2

4. Simplify the right side of the equation by dividing each term by 2.
(x + 14)/2 = y^2 + 6y - 14

5. Now we have a quadratic equation in terms of y. To solve for y, we need to use the quadratic formula: y = (-b ± √(b^2-4ac))/2a
In this case, a = 1, b = 6, and c = -14. Substituting these values into the formula, we get:
y = (-6 ± √(6^2-4(1)(-14)))/2(1)
y = (-6 ± √(36+56))/2
y = (-6 ± √92)/2
y = (-6 ± 9.6)/2

6. This gives us two possible values for y:
y = (-6 + 9.6)/2 = 1.8
y = (-6 - 9.6)/2 = -7.6

Therefore, the inverse of the given equation is:
f^-1(x) = 1.8 or -7.6

I hope this helps! Let me know if you have any further questions. Good luck with your algebra studies!