sorry this isn't hp but i really need your help guys.

Can all quadratic equations be expressed in factored form,explain?

What does the "a" mean(stand for)in the equation
y=a(x-s)(x-t)?

If the vertx is 4 , and the 2 zeroes are 1 and 5 how would you write it in standard form?

is there a way to check and see your answer is write when u find the value of "a"?

thanks

The best was way to dump someone:
"Hey baby welcome to dumpsville , population - you"
- The simpsons

"a" doesn't really mean anything -- it effects the shape of the parabola, its a stretching factor.

"Not everything that can be counted counts, and not everything that counts can be counted."
- Albert Einstein (1879-1955)

not all quadratic equations can be factored

if it doesn't factor, try this formula to find the zeroes:

assuming the quadratic equation is in the form
ax squared + bx + c


x= -b + or - sq. root of (b squared -4ac)
--------------------------------------
2a


you need the plus of minus to find BOTH zeroes

it is a complicated formula but it has the advantage of ALWAYS working.


and the "a" in your other formula only tells you whether the parabola will open up or down

--
If you break a crumb in half you have two crumbs, not two half-crumbs. Doesn't this violate some law of physics?

WOW, finally, my maths A-level comes in useful! Well, ok this isn't A-level work, but still.

All equations can be factorized, BUT, some will come up with OUTRAGEOUS fractions, that is where "completing the square" and "Quadratic formula" come in.

As Pinchy explained, the quadratic formula is rather complicated, but once known, it can solve all equations.

The best way to explain the "a" is (as pinchy also said) whether the vertex is a minimum point (meaning the parabola opens up), or a maximum point (meaning the parabola opens down) on the graph.


Ok, the vertex bit....
If the vertx is 4 , and the 2 zeroes are 1 and 5 how would you write it in standard form?

If the two zeroes are 1 and 5, then

(x-1)=0 and (x-5)=0
This means, that when y=0, x will either equal 1 or 5. - These are when the graph crosses the x axis!
When factorising, you must always have one side equaling zero.
(side note... {2} means squared.)
so, your equation will be...
0 = 4(x-1)(x-5)
0 = 4(x{2} - x - 5x + 5)
0 = 4(x{2} - 24x + 20)
0 = 4x{2} - 24x + 20

BLAH.... I am a bit miffed as to standard form, as I always knew it as y=mx+b but, there is x squared, and I forget starndard form for that. I THINK!!!! That that standard form is...

Y=ax{2}+bx+c
And for this equation that would be...
Y = 4x{2} - 24x + 20

is there a way to check and see your answer is write when u find the value of "a"?

ok, this is simple... take out the four and replace is it with A.

Y=ax{2}-24x+20
Now, substitute in a point you know... (one of the roots.) So, use (1,0) as you know that is a root.
Put in (1) for every X and 0 for the Y
so you get...
0=a(1){2}-24(1)+20
Now, the only unknown is A.
0=1a-24+20
Isolate A
4=1a
(divide by the number in front of the A, though as it's one, you don't need to.)
4=a


The shorter way, is to just take your equation
y=4x{2}-24x+20 and substitute in a root. - If the sides equal each other, it is correct.

OK, I hope that wasn't too confusing.

Thanks alot

The best was way to dump someone:
"Hey baby welcome to dumpsville , population - you"
- The simpsons