sorry maths - algebra

[15goddess15]

(2=squared)

write y=x2-5x+4 in the form of y=(x-a)2+b

??

[15goddess15]

is it

y=(x-5)2+4
?

[Muppit]

it sure is, but do you understand why?

[Muppit]

Ooops, no it's not...

[ladyalex]

Is it not

Y=(x-2)squared -x

(x-2)squared = xsquared -4x +4
so if you want xsquared -5x +4 you would need to take off another x

Or has my school algebra deserted me ?

[Suzyboo]

(x-2.5)2-2.25

Yours would expand to x2-10x+29

[Suzyboo]

ladyalex, the purpose is to produce all of the x terms from the expansion of the bracket - b must only be a constant - hence the need for a decimal/fraction in the bracket

[ladyalex]

Thanks suzyboo

[Buenchico]

Rather than just give you the answer, please allow me to try providing an explanation. (Then you'll be able to answer similar questions).

I'll denoted 'squared' in the same way that you've done.

Take a look at what (x-3)2 is equal to. The answer is x2 -6x +9.
Note that the coefficient of x (i.e. -6) is twice what's inside the bracket (i.e. -3). That will always be true with similar expressions. e.g. (x-5)2 = x2 -10x +25

In the expression you're starting with, the coefficient of x is -5. We know that must be twice the number inside the bracket, so that number must be -2.5.

So we've now got this:
y = x2-5x+4 = (x-2.5)2+b

If we multiply out that right hand term we get this:
y=x2-5x+4 = x2-5x+6.25+b

That gives us b + 6.25 = 4
<=>b = -2.25.

Thus y = (x-2.5)2 -2.25

Chris

[factor-fiction]

Good answer from Buenchico. I just wanted to show it's possible to set these out using the symbols such as x�. (The alternative way to represent squared is to use x^2)

y= x�-5x+4
y= (x-a)�+b

so:
x�-5x+4 ≡ (x-a)�+b
≡ x�+a�-2ax +b

Comparing coefficients of x :
-5 = -2a
so a=2.5

Comparing the 'constants':
4 = a� +b
= (2.5)� +b
= 6.25 + b
so b= -2.25

So, as Buenchico says:
y = (x-a)�+b
= (x-2.5)� -2.25

[Rev. Green]

That is useful, factor30. How did you show "squared"?

[factor-fiction]

Hello Rev. Green- to type symbols such as x� ≈ ∮� π�θ⁴ on AB I just type the response in Word (using insert symbols) and then cut and paste into my AB response

[Rev. Green]

Thaπks fa�tor30