Could someone please translate these equations and explain the steps for doing it?

y = x² - 8x + 15

y = 3x² + 25x + 42

Thanks. (Wink)

- May 29th 2008, 09:26 AMmathdonkeyNeed help translating standard form quadratic equations into factored form?
Could someone please translate these equations and explain the steps for doing it?

y = x² - 8x + 15

y = 3x² + 25x + 42

Thanks. (Wink) - May 29th 2008, 09:59 AMTKHunny
It's not magic. You just have to look.

x² - 8x + 15 =

Obvious part:

(x __ ___)(x __ ___)

Factors of 15

1,15

3,5

That's it.

Can one get 8 from these factors?

1+15 = 16 -- Nope.

1-14 = -14 -- Nope

3-5 = -2 -- Nope

3+5 = 8 -- Yes!!

(x __ 3)(x __ 5)

15 > 0, so 3 and 5 need the same sign.

-8 < 0, so both must be negative.

x² - 8x + 15 = (x - 3)(x - 5)

You do the other one. - May 29th 2008, 10:01 AMTheEmptySet
I'm guessing you mean in vertex form, that is,

To do the we need to complete the square, to do this we take half of the linear coeffeint and square it.

So the linear coeffeint is half of it is and now we square it to get This is what we need to complete the square.

We will now add zero to the euqation in the form of

so we get

Will will now rearrange the terms to get

Grouping the first three terms together and factoring gives

So we get

We can now identify a, h, and k

a=1 h=4 and k=-1

So we know that the vertext is located at the point and the the parabola opens up because a is postitive.

I hope this helps and is what you wanted.

If so here is a hint for #2 factor like this

and try to adapt the method used above.

(Rock) - May 29th 2008, 10:11 AMmathdonkey
How do I know it's (x - 3)(x - 5) and not (x - 5)(x - 3)?

Quote:

Originally Posted by**TKHunny**

- May 29th 2008, 10:34 AMIsomorphism
- May 29th 2008, 10:48 AMmasters

Multiplication is commutative, so (x - 3)(x - 5) = (x - 5)(x - 3)

To factor this trinomial, first multiply leading coef. times constant:

Result: 126

Find two factors of 126 that add up to the middle term's coef. of 25.

That'd be 18 and 7.

Replace the middle term with these two factors:

Factor by grouping:

- May 29th 2008, 10:59 AMmathdonkey
- May 29th 2008, 12:04 PMmasters
Swapping the binomials will not have an effect. However, if you were to multiply by -1, then the parabola would open in the opposite direction. The vertex would change, but the x-intercepts would be the same.

Did you need to see in vertex form? You can determine the zeros from the factored version in my previous post. They are - May 29th 2008, 05:53 PMmathdonkey
- May 29th 2008, 06:33 PMmathdonkey
I'm having some trouble with this question too.

y = 20x² - 3x - 9

I get this:

= 20x² + 12x - 15x - 9

= (20x² + 12x) (-15x - 9)

= 2(10x + 12x) 3(-5x - 3)

(I don't know what to do next)

But the answer is supposed to be:

y = (4x - 3) (5x + 3)

What am I doing right/wrong? - May 29th 2008, 06:57 PMTKHunny
- May 29th 2008, 07:03 PMTKHunny
Just make a catalogue.

20

1*20

2*10

4*5

9

1*9

3*3

-9 < 0, so opposite signs

We're looking for a -3

1*1 - 9*20 -- too big

1*20 - 9*1 = 11

1*3 - 9*3 = -26

2*1 - 10*20 -- too big

2*20 - 10*1 = 30

2*3 - 10*3 = -27

4*1 - 5*20 -- too big

4*20 - 5*1 = 75

4*3 - 5*3 = -3 -- Aha!!!!

(4x - 3)(5x + 3)

Be systematic.

Note: I started witht the most extreme values, just for the practice. I don't recommend that if you REALLY want the quickest path to the answer. - May 29th 2008, 08:02 PMmathdonkey
Sorry TKHunny, I'm a little confused by your method.

Using those numbers I can write (4x - 3) (5x + 3). Is that all I have to do?

Quote:

We're looking for a -3

1*1 - 9*20 -- too big

1*20 - 9*1 = 11

1*3 - 9*3 = -26

2*1 - 10*20 -- too big

2*20 - 10*1 = 30

2*3 - 10*3 = -27

4*1 - 5*20 -- too big

4*20 - 5*1 = 75

4*3 - 5*3 = -3 -- Aha!!!!

- May 30th 2008, 05:09 AMmasters
- May 30th 2008, 07:10 AMmathdonkey