Parent function: y=x2
a, h, and k:
In the equation y = a(x-h)^2 + k
a: This coefficient affects the vertical stretch or compression and direction of the parabola in this equation. here, a = 4 which means the parabola is narrower and opens upwards
h: This value represents the horizontal shift here, h = 3, the parabola shift 3 unit to the right.
k: This value shows that vertical shifts. the k = -6 means the parabola shift 6 units downward.
compared to the parent function y = x^2, the parabola is vertically stretched by a factor of 4
shifts 3 units to the right, and 6 units downwards.
Self-Assessment
- Multiple Representations: In this assignment, I have presented the same mathematical concept by providing both the equation and the graph of the parabola. the graph demonstrates the effects of the parameters a, h and k on the parabola.
- Mathematical Vocabulary: I used mathematical terms like “vertical stretch”, “horizontal shift” and “vertical shift” to explain how the parameters a, h and k effects the shape and position of the parabola
- Formatting for Clarity: I organized the information by labelling each part of the assignment. I have made it easier to follow the explanations and understand the transformations applied to the parabola