in paper 1 question 14 part c i did it completely different to everyone else
most people used the values 180 and 0 and subbed them in but I did it like this:
if you multiply the factors of a line you get the equation
we can get the factors by getting the roots and we know the roots of this are 3 because it told us the graph was symmetrical. So therefore the factors are x-3 and x-3 I just multiplied these out and it matched the function given just with numbers instead of letters.
I don't know a single person who did it this way but!! I started doing it the same way as everyone else but my numbers seemed weird and I thought because the bothered to say that the graph was symmetrical that they wanted it done this way. I got 9 out for C not 180 but i feel that it could be something to do with multiples which I know you cover in the leaving cert course. Is this right and if not will i get some marks for it? Thanks!!
You will probably get about 80% of the marks as you only left out one step.
The graph had a repeated root, i.e. The turning point was a root (3,0) so X=3 was the root of the function which gives out the factors to be (X-3)(X-3), I.e. (X-3)^2
but what you failed to take into account that quadratics can have the same roots but can be scaled, so the quadratic was of the form a(X-3)^2 where a is the scale factor of the graph. In this case a=20, which gives out c=180
The mistake you made was that you forgot that the height at noon (X=0) was 180 and thus the constant (c) was equal to the y intercept.
If you had taken this into account you would get c=180 and as a result every constant in the function rule must also be multiplied by 20, I.e. 180 divided by 9
To solve a quadratic where the roots are rational numbers you can factorise it and let the roots equal to zero and solve.
The equation 20x^2-120x+180= 0 can be factorised to 20(X-3)^2=0 so (X-3)^2=0 (divide both sides by 20) and so X-3=0 as when a factor is squared there is a repeated root. Solve X-3=0 we get X=3.
Hopefully from the example above you can see that equations can be multiplied by a factor and will still have the same roots
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This is a simultaneous equation-a father and his son have a combined age of 52.8 years ago the father was 8 times the sons age .write and equation in x and y