Standard Form of a Quadratic Equation

When a quadratic equation is in the form  f(x)  =  a(x - h)² + k ,  the vertex is  (h, k)

 

For this problem, they tell us the vertex is  (-1, 5) , so we know that

 

f(x)  =  a(x - -1)² + 5

 

f(x)  =  a(x + 1)² + 5

 

We know it goes through the point  (2, -13) , which means  f(2) = -13

 

f(2)  =  a(2 + 1)² + 5       And  f(2) = -13

 

-13  =  a(2 + 1)² + 5

 

-13  =  9a + 5

 

-18  =  9a

 

-2  =  a

 

Now we've found  a  , so we know that

 

f(x)  =  -2(x + 1)² + 5            And here's a graph to check it.