Quadratic function and principle of zero: Find x so f(x) = 3x^2 - 4x = 4

[DustinC]

Hey guys. I've got this math problem that I don't understand. So here it goes.
Learning about principle of zero, and the math book gives me this example problem. The whole point of the principal of zero in this example is to factor the equation, and then find the value of x if the equation is split up into 2 terms and one is made to equal zero, so that it gives me the value for x. Best way I can explain it guys.

"given that f(x) = 3x^2 - 4x, find all values for x for which f(x) = 4"

* I used the ^ to connotate the x being squared (3x squared)


Now what I don't get is why I'm finding values for x that makes f(x) = 4

Isnt the whole point of this principle of zero thing to put zero on one side? Why am I finding numbers that make f(x) = 4?

The answer they supply for the question is either x =(negative 2/3) or x = 2

 

[mmm4444bot]

… given that f(x) = 3x^2 - 4x, find all values for x for which f(x) = 4 …

Now what I don't get is why I'm finding values for x that makes f(x) = 4

Isnt the whole point of this principle of zero thing to put zero on one side?

Not put. You want to get zero on one side (and a new quadratic polynomial on the other side). In other words, you want to get a quadratic equation in standard form:

Ax^2 + Bx + C = 0

I would begin by writing the given information, that function f equals 4:

3x^2 - 4x = 4

Now, what can you do to get standard form?

 

[DustinC]

Not put. You want to get zero on one side (and a quadratic polynomial on the other side). In other words, you want to get a quadratic equation in standard form:

Ax^2 + Bx + C = 0

I would begin by writing the given information, that function f equals 4:

3x^2 - 4x = 4

Now, what can you do to get standard form?

OK but why am I putting = 4 on the other side of that equation in the first place? Shouldn't I be putting = 0?
Where did the need for the 4 come in?

 

[DustinC]

Not put. You want to get zero on one side (and a quadratic polynomial on the other side). In other words, you want to get a quadratic equation in standard form:

Ax^2 + Bx + C = 0

I would begin by writing the given information, that function f equals 4:

3x^2 - 4x = 4

Now, what can you do to get standard form?

Oh wait I think I get it. Dumb move. So I was directly asked to find values for x where f(x) = 4.

I had assumed they had used 4 for a specific reason that they got directly from the quadratic equation. But I guess they could of used any number for f(x) and asked me to find values for x that gave that f(x)

I just didn't get that.

 

[mmm4444bot]

… But I guess they could of used any number for f(x) and asked me to find values for x that gave that [value for] f(x) …

You got it!

They chose four because it's one of the numbers which leads to a quadratic that factors nicely. :cool:

Next, are you going to Complete the Square, Factor by Grouping or use the Quadratic Formula?

 

[DustinC]

You got it!

They chose four because it's one of the numbers which leads to a quadratic that factors nicely. :cool:

Next, are you going to Complete the Square, Factor by Grouping or use the Quadratic Formula?

I'd factor by grouping. It makes sense now. I just skimmed over the question too fast I think.

 

[DustinC]

You got it!

They chose four because it's one of the numbers which leads to a quadratic that factors nicely. :cool:

Next, are you going to Complete the Square, Factor by Grouping or use the Quadratic Formula?

Thanks for the help!