f(x) = x² : the parent function
f(x) = 1/5x² – 2 : the parabola that demonstrates a vertical stretch (dashed line)
f(x) = 2(x-6)²-1 : the parabola that demonstrates a vertical shift down
f(x) = 1(x+4)²+1 : the parabola that demonstrates a horizontal shift left
f(x) = 3(x-8)²+1 : the parabola that demonstrates a horizontal shift right
f(x) = 1(x+6)²+2 : the parabola that demonstrates a vertical shift up
f(x) = 5(x+9)²+4 : the parabola that demonstrates a vertical compression
Transformation Explanations
- The first parabola in the list above is the parent function, which is the simplest parabola and has not been changed by any transformations.
- The second parabola demonstrates a vertical stretch, which means it has a wide opening, and this is due to the a value. The smaller the a value, the wider the parabola will become. f(x) = 1/5x² – 2 : 1/5 represents the a value, and if this was changed to a value of 4, it would become narrower. If |a| > 1 the parabola will have a narrower shape than the parent function,
- The third parabola demonstrates a vertical shift down, which occurs when the k value is negative. f(x) = 2(x-6)²-1 : -1 is the k value.
- The fourth parabola demonstrates a horizontal shift left, which is depending on the h value being negative. f(x) = 1(x+4)²+1 : The h value became positive, because a negative value was replaced in the spot of h in the equation f(x)=a(x-h)²+k, which canceled out the negative of the h, making it a positive value.
- The fifth parabola demonstrates a horizontal shift right, which is due to the h value being positive. In the equation f(x)=a(x-h)²+k, adding a positive value to h will keep it negative in the equation.
- The sixth parabola demonstrates a vertical shift up, which is when the k value is positive. f(x) = 1(x+6)²+2 : the 2 is positive, so it shifts the parabola upwards.
- The seventh parabola demonstrates a vertical compression, which means that it has a narrow opening, which is due to the a value. The larger the a value , the narrower the parabola will become. f(x) = 5(x+9)²+4 : if the 5 was changed to a 1, this would widen the opening of the parabola. If 0 < |a| < 1 the parabola will have a wider shape than the parent function.
Communication Core Competency Reflection
While working on this assignment, I made sure to clearly demonstrate my understanding for transforming parabolas by keeping my parabolas organized on the graph and colour coding each parabola to differentiate them from one another. To avoid excessive overlapping, I increased and decreased certain values to lay out each parabola neatly, using my knowledge that I have learned in class. When creating my edublog, I carefully colour coded each of the equations to match them to the parabola, making it easier to understand. I clearly explained the purpose of each parabola that was graphed, to make sure it wasn’t too difficult to understand, while still using relevant math vocabulary to describe each purpose.