Question

How do you graph parabolas $?$

Answer 1

Graphing parabola :

The equation of a parabola is given by:

$f(x)=a{x}^2+bx+c$

To graph a parabola we need to find the vertex by using the formula,

$x=\frac{-b}{2a}$ and $f\left(\frac{-b}{2a}\right)$

Now, start finding the value of $f\left(x\right)$ for different values of $x$.

For eg: the equation of parabola is $f(x)=3x^2+2x+1$
$x=\frac{-2}{6}=\frac{-1}{3}$

$\begin{array}{rcl}f\left(\frac{-1}{3}\right)& =& 3{\left(\frac{-1}{3}\right)}^2+2\left(\frac{-1}{3}\right)+1\\ & =& \frac{1}{3}-\frac{2}{3}+1\\ & =& \frac{2}{3}\end{array}$

Now finding the values of $f\left(x\right)$ for different values of $x$.

$\begin{array}{cccc}x& 0& 1& -1\\ f(x)& 1& 6& 2\end{array}$

Hence, the graph of parabola $f\left(x\right)$ is as follows