Final conclusion : Each of the of the 3 function patterns follows the equation f

Question

Final conclusion : Each of the of the 3 function patterns follows the equation   f(x) = a(x - h)^2 + k. Explain how the a , h and k, make the parabola shift

Function Pattern 1 : Type in x2 in the calculator (Desmos.com/calculator ) and hit enter. This is your standard function, the square function. Now punch in each of the following equations: x^2 +2 , x^2+5 , x^2 +7 , x^2 - 2 , x^2-4 , x^2-8 , x^2 - 1 , LOOK FOR A PATTERN. WHAT IS HAPPENING TO EACH PARABOLA ? WHY? DRAW SOME CONCLUSIONS. x^2+1 Do not punch in  y = x^2 +2, just punch in the x^2 + 2. this also applies to the rest of the functions. For all of these patterns, your graphs will look like a parabola, which is shaped like the latter " U ". If you get something else, then something is wrong.

Function Patterns 2 :    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 a pattern, what is happening to each parabola? why ? draw some conclusions. Make sure thet the 2 is an exponent and is outside of the paretheses.   

Function pattern 3 : 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      Thank you

Explanation / Answer

Function Pattern 1 : X^2 is standard equation.adding an integer to X^2 will move the function upward and downward on y-axis. positive interger will move the function upward and negative integer move the function downward.

Function Pattern 2 : function will shift the function left and right on x axis. adding positive interger will shift the function left and adding negative integer will shift the function right on x axis.

Function Pattern 3: function will compress and expand .on multiplying the integer to the function ,function will compress and divding the function by an integer, function will expand.

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