The standard form of the quadratic function is
y=ax∧2+bx+c
In order to determine the unknown parameters we will picked up three points from the given graph.
A(-1,-3) , B(0,-1) and C(1,5)
When we replace B coordinates in the quadratic function we get
-1= 0*a+0*b+c => c=-1 => y=ax∧2+bx-1
After that we will replace A and C coordinates in the quadratic equation and get
-3=a(-1)∧2+b(-1)-1 => -3=a-b-1 => a-b=-2
5=a*1∧2+b*1-1 => 5=a+b-1 => a+b=6
a-b=-2
a+b=6
When we add first equation to the second we get
2a=4 => a=2 When we replace a=2 in the first equation we get b=4
The quadratic function for the given graph is
y = 2x∧2+4x-1
Good luck!!!
