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Question

consider a quadratic function form y=a(x - p)^2 + q. explain how its graph will change for each transformation described below. Sketch of needed! 

a) the sign of a is changed.

b) the value of q is decreased by 3.

c) the value of a is less than one, but is still positive.

d) the value of p is increased by 2.

e) the value of p is decreased by 5, the value of q is increased by 3, and a is negative.

Answer 1

Given quadratic function form y=a(x - p)^2 + q 

(a)

Let us consider  two quadratic functions with different sign of 'a' , to observe its behavior  .

y = -4(x-2)^2 +5     and  y = 4(x-2)^2 +5  

Now graph the functions

From the graph we can conclude that the graph will be inverted when we change the sign of  'a' .

Answer 2

Quadratic function form y=a(x - p)^2 + q 

(b)

Let us consider  two quadratic functions with the  value of q decreasesd by 3 with another , to observe its behavior.

y = 4(x-2)^2 +5     and  y = 4(x-2)^2 +2

The vertex will decreased by 3 when the value of q decreasesd by 3 .

Now graph the functions

From the graph we can conclude that the vertex will be decreased by 3 when the value of q decreasesd by 3.

Answer 3

(c)

Let us consider  two quadratic functions with different values of 'a' in which of those one value of a is less than 1 , to observe its behavior.

y = 4(x-2)^2 +5     and  y = 0.64(x-2)^2 +5

If the coefficient of x² gets smaller, the parabola becomes thicker (wider).

Now graph the functions :

From the graph we can conclude that the parabola becomes wider when the coefficient of x² gets smaller .

Answer 4

(d)

Let us consider  two quadratic functions with different values of 'p'  and one function is the value of 'p' increasesd by 2 with another , to observe its behavior.

y = 4(x-2)^2 +5     and   y = 4(x-4)^2 +5

When the value of 'p' increases then the  graph shifted to right .

Now graph the functions :

From the graph we can conclude that the graph shifted to right when the value of 'p' increases .

Answer 5

(e)

Let us consider  two quadratic functions with different values of 'p' ,'q' and negative sign of 'a'.

y = 4(x-7)^2 +5       and     y = -4(x-2)^2 +8 

When we decrease the value 'p' , the graphs moves to left .

When we increase the value of  'q'  , the vertex will increase .

When we change the sign of  'a' the graph is inverted . 

Now graph the functions :

All the changes are reflected in above graph .