How to write the quadratic function.

[mathlearn]

Write a quadratic function y whose maximum value is 4 and the axis of symmetry of the graph is x=-2.

Suggestions?

 

[MarkFL]

Where should the vertex be? Recall the vertex form of a quadratic may be written as:

\(\displaystyle y(x)=a(x-h)^2+k\)

where the vertex is at $(h,k)$. Since the quadratic is to have a maximum, what can we say about $a$?

 

[mathlearn]

Where should the vertex be? Recall the vertex form of a quadratic may be written as:

\(\displaystyle y(x)=a(x-h)^2+k\)

where the vertex is at $(h,k)$. Since the quadratic is to have a maximum, what can we say about $a$?

Since the quadratic is to have a maximum , 'a' should be a negative.

\(\displaystyle y(x)=-a(x+2)^2+4\)

Correct?

 

[MarkFL]

Since the quadratic is to have a maximum , 'a' should be a negative.

\(\displaystyle y(x)=-a(x+2)^2+4\)

Correct?

Yes, as long as $0<a$, then you have correctly given the family of quadratics that meet the stated criteria. :D

Alternately, you could state:

\(\displaystyle y(x)=a(x+2)^2+4\) where $a<0$.

 

[mathlearn]

Thank you very much :)