Function Pattern 1 Type in x12 Now change the number inside

Function Pattern 1 : Type in (x+1)^2 Now change the number inside the ( ). Change the number to 4, 7, -2, -4, -6, 5, 3. [ (x+4)^2 or (x+7)^2 for example ]. LOOK FOR PATTERN. What is happening to each parabola ??? Why ? Draw some conclusions. Make sure that the 2 is an exponent and it is outside of the paretheses. Function pattern 2 : Again, draw some conclusions. Punch in the following. 2x^2, 5x^2,   8x^2,   15x^2,    1/2x^2,    1/5x^2,    1/10x^2

Function pattern 3 :  Punch in the equations below and draw some conclusions. Create more if you still cannot see a pattern.    - x^2 - 2x^2 ,       - 7x^2 ,      -13x^2 ,   - 5x^2                                                         desmos.com/calculator

Solution

FunctionPattern 1 : (x +1)^2

In comparsion to parent function y = x^2

(x +4)^2 horizontal shift to left by 4 units

(x +7)^2   horizontal shift to left by 7 units

( x -2)^2   horizontal shift to right by 2 units

( x -4)^2  horizontal shift to right by 4 units

So, we can see that for ( x+a)^2 function y= x^2 is shifted to left by a units and for (x -a)^2  function is shifted to right by a units .

Stretching & Shrinking of function:

C•f(x), where C is a real number > 0 If C > 0, then f(x) has a vertical STRETCH by a factor of C units. If 0 < C < 1, then f(x) has a vertical SHRINK by a factor of C units.

Function Pattern 2 :y = 2x^2 ---> function y= x^2 is vertically stretched i.e. graph becomes skinnier by 2 units

y = 5x^2 ---> function y= x^2 is vertically stretched i.e. graph becomes skinnier by 5 units

y = (1/2)x^2 ---->  ---> function y= x^2 is vertically shrink by 0.5 units i.e. graph becomes wider

y = (1/10)x^2 --->  ---> function y= x^2 is vertically stretched by 0.1 unitsi.e. graph becomesmore wider than the previous graph y= x^2 .

Function Pattern 3 : y = -x^2 ---> function y= x^2 gets inverted along x axis

y = -2x^2 ----> function y= x^2 gets inverted along x axis and is vertically stretched i.e. graph becomes skinnier by 2 units.

y = -13x^2 ----> function y= x^2 gets inverted along x axis and is vertically stretched further as compared to previous one i.e. graph becomes skinnier by 13 units.