MHB How to write the quadratic function.

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

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

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

where the vertex is at $(h,k)$. Since the quadratic is to have a maximum, what can we say about $a$?
 
MarkFL said:
Where should the vertex be? Recall the vertex form of a quadratic may be written as:

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

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.

$$y(x)=-a(x+2)^2+4$$

Correct?
 
mathlearn said:
Since the quadratic is to have a maximum , 'a' should be a negative.

$$y(x)=-a(x+2)^2+4$$

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:

$$y(x)=a(x+2)^2+4$$ where $a<0$.
 
Thank you very much :)
 

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