solving quadratics, plugging into fcns, finding domains

I need to find the solution(s) to this equation.

1: 5(X+3)^2+2=8

I know that it is a non-real solution but I can't get much further than that.

Also, I could use some help with these problems as well.

2: If I wanted to find when 50% of the insurance companies used drug tests on their employees, using the regression f(x)=-0.64x^2 +14.47t-3.40, how might I go about doing this?

3: And lastly, how can I find the range and axis of symmetry for g(t)=-3t^2-6t-8?

My sincerest thanks to whoever can help me out with this, I'm a total idiot when it comes to math!

Re: Need help with quadratics

Duddles said:

I need to find the solution(s) to this equation.

5(X+3)^2+2=8

Hint: Get 0 on the right side (by subtracting 8 from both sides of the equation, just like you did when you were solving equations for a varaible) and then factor the polynomial that results on the left side. You might have to expand it, combine like terms, etc., to make factoring it easier. I hope you went to school on the days when someone taught you those particular skills, because they're going to come in handy here.

I know that it is a non-real solution but I can't get much further than that.

Much further than what?

Also, I could use some help with these problems as well.

If I wanted to find when 50% of the insurance companies used drug tests on their employees, using the regression f(x)=-0.64x^2 +14.47t-3.40, how might I go about doing this?

It wants to know the value of x when the polynomial equals 0.5. Set it equal to 0.5 (instead of f(x)), write 0.5 there, get the left side to 0 with some arithmetic, factor it, which will give you two solutions for x, but I suspect one will not make any sense in the context of the problem.

And lastly, how can I find the range and axis of symmetry for g(t)=-3t^2-6t-8?

What is the general equation for a quadratic, in terms of a, h, and k? What do those parameters represent?


My sincerest thanks to whoever can help me out with this, I'm a total idiot when it comes to math!

There is no such thing as an idiot in math. Some of this is hard stuff, especially if you haven't tried anything but asking people on a math help board how to do the problems. Please write back with your work so far, based on the questions I asked here, and we'll help you along the rest of the way. Promise.

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Re: Need help with quadratics

I apologize.

I really have a difficult time with math. I've failed my university required class twice already and it's the only reason I've yet to graduate. I was placed in a remedial math class during my first year of college and I didn't do so hot in that either. I don't often know what is the right question to ask when I'm having difficulty, so I apologize for my ambiguity.

For the first equation, my homeworks asks me to write out any complex situations in (a+bi) form however when I go through the examples in my algebra book, there really isn't an example that is similar to the given problem to help me sort it out. What I attempted to do was get it into the quadratic form, so I had 5x^2+219=0. So then I My calculator has a quadprogram in it and it said this equation had a non-real solution, so I used the quadratic formula to try and sort out the answer. I ended up with the answer plus or minus square root i -4380/-10950... He said that we don't have to simplify beyond that, if that makes any sense.

I obviously don't feel all that confident in my answer. My professor didn't really go over too much about factoring (as he said that it takes too long) and said that we should be able to do all of the problems without doing it, so I tried to follow the assigned chapter in the book and my notes from class.

As for the second problem I asked for help with, can I assume that if I put the equation into the Y1= on my TI-83 calculator and then put 0.5 into the Y2= that I should be able to find the answer to this using the graph and point of intersection? According to my table it is somewhere between 4.6 and 4.9 years but that doesn't seem accurate to me.

And the last problem I'm not too worried about as it's a bonus question as he's yet to go over that material. Just wanted to see if we remembered anything from high-school (or in my case, my remedial college math class).

Sorry again, I hope this sheds a little light on my thought process, even if it probably is all wrong.

Re: Need help with quadratics

Well, now I can see where the problem is. You say that first quadratic is 5 x^2 + 219. 219?? How can those numbers possibly make a number that big? When you got that, a little red flag should have gone up, if you were thinking about what you're doing. When an answer doesn't make sense like that, go back and start over. In this case, you have to get that expression in \(\displaystyle a x^2 + b x + c\) form. Otherwise, this is pointless to go any further.

I'll get you started, but you need to take a few steps from here. Remember, keep evaluating it until you get it in that form. You may have to combine like terms, apply the distributive property, etc. This stuff all comes back to haunt you if you don't get it right at the beginning, so let's spend a little time...

\(\displaystyle 5 (x + 3)^2 + 2 = 8\)

\(\displaystyle 5 (x^2 + 6 x + 9) + 2 = 8\)

All I did was first-outer-inner-last (FOIL). Do you remember that? (x + 3)^2 = (x + 3) (x + 3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9. Can you go a little from here? It's not close to 5 x^2 + 219. I think the solution below is more elegant, but if you're having trouble evaluating polynomials, I thought it best to go back to the beginning.

Re: Need help with quadratics

Duddles said:

I need to find the solution(s) to this equation.

5(X+3)^2+2=8

I know that it is a non-real solution but I can't get much further than that.

Also, I could use some help with these problems as well.

If I wanted to find when 50% of the insurance companies used drug tests on their employees, using the regression f(x)=-0.64x^2 +14.47t-3.40, how might I go about doing this?

And lastly, how can I find the range and axis of symmetry for g(t)=-3t^2-6t-8?


My sincerest thanks to whoever can help me out with this, I'm a total idiot when it comes to math!

Click to expand...

I'm not sure on what basis you say that 5(x + 3)^2 + 2 = 8 has non-real solutions.

You've got a nice perfect square on the left side: (x + 3)^2

Get everything else on the other side, and then take the square root of both sides.

Start by subtracting 2 from both sides of the equation:

5(x + 3)^2 + 2 - 2 = 8 - 2

5(x + 3)^2 = 6

Divide both sides of the equation by 5, to get (x + 3)^2 by itself:

5(x + 3)^2 / 5 = 6/5

(x + 3)^2 = 6/5

Now...take the square root of both sides:

sqrt[(x + 3)^2] = + sqrt(6/5)

x + 3 = + sqrt(6/5)

Add -3 to both sides:

x + 3 + (-3) = -3 + sqrt(6/5)

Now...those are definitely REAL solutions....

Re: Need help with quadratics

Gee Duddles, you seem to be trying to play hockey on shoes instead of skates!
Seems to me you are unaware of the basics.
Can you solve this quadratic equation: 2x^2 - 7x - 15 = 0