Vertex form is defined as:
f(x)=a(x-h)^2+kf(x)=a(x−h)2+k
The way to find the vertex is to use -b/(2a)−b2a (for the hh value), and then plug that number in for xx in the original quadratic (for the kk value).
Now that we know that, we can solve for our hh value:
-b/(2a) => -(-3)/(2(5)) => 3/10−b2a⇒−−32(5)⇒310
Now that we have our hh value, we can plug it in for xx in the quadratic:
5(3/10)^2-3(3/10)+15(310)2−3(310)+1
=> 5(9/100)-9/10+1 ⇒5(9100)−910+1
=> 45/100-9/10+1 ⇒45100−910+1
=> 45/100-90/100+100/100 ⇒45100−90100+100100
=> -45/100+100/100 ⇒−45100+100100
=> 55/100 ⇒55100
=> 11/20 ⇒1120
Now we have our kk value! We can now switch the quadratic from standard form, to vertex form:
f(x)=5(x-3/10)^2+11/20f(x)=5(x−310)2+1120
