EFFECT OF COEFFICIENT OF X ON PARABOLA VERTEX (b>0)
Write-pair-share

Consider the general form of a quadratic function,  

    or     ,    where .

Part 1
If the coefficient b is increased in value, how will this increase affect the position of the vertex of the parabola?  

For the sake of simplicity, you may assume that both a and c are fixed values and that a=1 and c=2.  (A similar analysis could be performed with a<0.)

The new vertex will be:

CIRCLE ONE:

A.	 LOWER AND TO THE RIGHT OF THE ORIGINAL VERTEX

B.  LOWER AND TO THE LEFT OF THE ORIGINAL VERTEX

C.  SAME POSITION AS THE ORIGINAL VERTEX

D.  HIGHER AND TO THE RIGHT OF THE ORIGINAL VERTEX 

E.  HIGHER AND TO THE LEFT OF THE ORIGINAL VERTEX

After making your decision concerning the possible answer choices, please discuss your conjecture with your nearest neighbor and explain to each other the underlying reasoning.  You don’t necessarily have to agree with each other’s assessment, but do have a candid discussion; you are free to change your initial reasoning in light of your neighbor’s explanation

Part 2
Afterwards, please record your conjecture and reasoning in written form; a single paragraph will be sufficient.  

Part 3
1.	Use the formula for the vertex of the parabola, , to algebraically analyze the effect of increasing the value of b on the position of the vertex.  You will need to expand the expression  in order to more easily see the effect on the 
y-coordinate of the vertex.  Please describe the key elements of your analysis.

2.	Do your calculations uphold your conjecture (from Parts 1 and 2) concerning the effect of increasing the value of b on the position of the vertex?  If not, please explain in more detail.