Algebra 2 quadratic function help

Question

write the equation of the quadratic function with roots -9 and -3 and a vertex at (-6,-1)

Answer 1

Hi Mi,

 

there is a form of the quadratic that we can use when we know the vertex

 

y = A(x -h)² +k   (where h and k are the values of the vertex

 

so  lets sub -6 and -1 for h and k

 

y =A(x + 6)² -1

 

and now we can find A using one of the roots

 

when x is -9 or -3 y =0

 

0 = A(-3 + 6)² -1

 

1 = A(3)³

 

1 = 9A

 

1/9 = A

 

the final equation is

 

y = (1/9)(x + 6)² -1

 

Hope this helps