Write the equation of the quadratic function whose graph is shown

Step 1
To find the equation of a quadratic function whose graph is,
shown and write it in the form
${\displaystyle f\left(x\right)=a{x}^2+bx+c}$
A quadratic function fin vertex form is written as
${\displaystyle f\left(x\right)=a{(x-h)}^2+k}$
where h and kare the x and y coordinates plot in the graph
Step 2
${\displaystyle y=a{(x-h)}^2+k,h=2,k=-4,x=4,y=0}$
${\displaystyle \Rightarrow 0=a{(4-2)}^2+(-4)}$
${\displaystyle 0=a{\left(2\right)}^2-4}$
${\displaystyle 0=a4-4}$
${\displaystyle a4=4}$
${\displaystyle a=1}$
${\displaystyle f\left(x\right)=1{(x-2)}^2-4}$
${\displaystyle =1(x^2-2x+4)-4}$
${\displaystyle =x^2-2x+4-4}$
${\displaystyle f\left(x\right)=x^2-2x}$