Solution assignment 09 Quadratic functions and graphs

Calculate the equation of the parabola going through the points $(0,0)$ , $(2,1)$ and $(1,3)$ .

The general equation of a parabola is:

$y=ax^2+bx+c$

We have to calculate the values of $a$ , $b$ and $c$ based on the fact that the given points lie on the parabola.

$(0,0)$ lies on the parabola, thus $c=0$ .

$(2,1)$ lies on the parabola, thus $1=4a+2b$

$(1,3)$ lies on the parabola, thus $3=a+b$

So we have two solve two linear equations with two variables $a$ and $b$ :

$4a+2b=1$
$a+b=3$

Multiply the second equation by $2$ and subtract the result from the first equation (in this way we eliminate $b$ ):

$2a=-5$

$a=-\displaystyle\frac{5}{2}$

If we substitute this value of $a$ in the second equation we get for $b$ :

$b=\displaystyle\frac{11}{2}$