Ok so i have this small project that i have to do where i'm given the four different type of functions and i have to find out what the pattern in each set it. I was able to figure out each pattern but now for the final part i'm asked how a,h and k would shift each parabola in this function:
f(x) = a (x - h)2 + k -2 being squared
I've posted the entire assignment as well as the part that i'm stuck on-the final conclusion-. I'd appreciate it if someone could lead me into the right direction without giving me the answer.
FUNCTION PATTERN 1
Type in x^2 in the calculator and hit Enter. This is your standard function, the square function.
Now punch in each of the following equations. I will type them the correct way instead of using the caret. Look for a pattern. What is happening to each parabola? Why? Draw some conclusions. If you are not yet ready to draw some conclusions, then punch in a bunch more similar equations.
x2 + 2 x2 + 5 x2 + 7 x2 -2 x2 - 4 x2 - 8 x2 -1 x2 + 1
x2 is x squared
You do not want too many graphs on the calculator at any one time.
For all of these patterns, your graphs will look like a parabola, which is shaped like the letter "U". If you get something else, then something is wrong.
FUNCTION PATTERN 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. If you are not yet ready to draw some conclusions, then punch in a few more equations.
FUNCTION PATTERN 3
Again, draw some conclusions. Punch in the following.
2x2 5x2 8x2 15x2 1/2x2 1/5x2 1/10x2
x2 means x squared
FUNCTION PATTERN 4
Punch in the equations below and draw some conclusions. Create more if you still cannnot see a pattern.
- x2 - 2x2 - 7 x2 -13x2 -5x2
x2 means x squared
FINAL CONCLUSIONS
Each of the first 3 patterns follows the equation f(x) = a(x - h)2 + k.
Now that you have seen the 3 patterns, explain how the a, h, and k make the parabola shift.
After you submit the above to me, try some of the other patterns listed below. Punch in a bunch of different numbers to watch the graph change. You now should be able to anticipate what is going to happen to each graph.
f(x) = This is the square root function.
f(x) = |x| This is the absolute value function.
f(x) = x3 This is the cube(cubic) function.
To get the square root, hit the sqrt key, which is below the word Clear.
To get the absolute vale, type abs(the number). For example, type abs(x) or abs(x+3).
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I had given him this answer originally:
If a was multiplied by anything inside the parenthesis and then squared, it would not create a shift. The value of (x - h)2, would shift the parabola to the right.The value of k, when positive makes the parabola shift to the right vertically.