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Question

consider a quadratic function in the vertex form y= a (x -p)^2 + q. Explain how its graph will transform for each chamge described below

a) the sign of a is changed form positive to negtive

b) the value of q is decreased by 2

c) value of 'a' decreased but still positive

d) the value of p is increased by 2.

Answer 1

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

(a)

Let us consider two quadratic functions with 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 2 with another , to observe its behavior.

y = 4(x-2)^2 +5     and  y = 4(x-2)^2 +3

The vertex will decreased by 2 when the value of q decreasesd by 2 .

Now graph the functions

 

From the graph we can conclude that the vertex will be decreased by 2 when the value of q decreasesd by 2.

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 .