-1
$\begingroup$

I'm having trouble finding the coefficients in this equation based on knowing where a parabola passes through at certain points.

Question:

By solving a system of $3$ equations in $3$ variables, find the coefficients in the equation of the parabola $y = \alpha + \beta x + \gamma x^2$ that passes through the points $(1, 1)$, $(2, 2)$ and $(3, 0)$.

  • 0
    We have $y=c(x-3)(x-b)$, from $1=-2c(1-b)$ and $2=-c(2-b)$ you'll be able to find $b$ and $c$. – 2017-01-29

1 Answers 1

0

you have $$a+b+c=1$$ $$4a+2b+c=2$$ $$9a+3b+c=0$$ multiplying the first by $-4$ and adding to the second we get $$2b+3c=2$$ (I) multiplying the first by $$-9$$ and adding to the last one we get $$6b+8c=9$$ (II) multiplying $(I)$ by $-3$ and adding to (II) we get $$-c=3$$ can you proceed?

  • 0
    Wonderful! That makes it a whole lot easier. Thank you, my friend. – 2017-01-29
  • 0
    that is not me but it is the so called Gauss algorithm – 2017-01-29