Parent equation: y=x^2

My equation: 𝑦=3(𝑥−4)^2+2

Desmos Graph of the parent equation:

Desmos graph of my equation:

The value of a, h and k that were added in my equation make a significant change to the original parabola. The original form of this function (the parent equation) does include a, h and k values. “A” value for the parent function is 1, but h and k value are 0. The “a” value changes the shape of the parabola from the parent function. For example, if the “a” value was negative my parabola would open downwards instead of up. For the parent function, a=1 so it would open upwards, for my parabola is 3 so the shape of my graph is upwards but narrower. “h” value, causes the parabola to move horizontally from the original point (parent function) depending on whether it’s negative or positive. If the “h” value is positive the graph moves to the right (Positive) from the origin point, and if the value is negative the graph moves to the left (negative) from the origin. For the parent function h value is 0 so the graph’s vertex is at 0. For my parabola the h value is 4 so the vertex is at 4. The “k” value determines where the graph starts vertically. In this case, my k value is +2 so the graph opens up when the y value is +2 instead of opening on 0, like the parent function.

Self assessment

1. Give an example from this assignment where you represented the same mathematical idea in multiple ways? I explained how the values of a, h and k are able to change a parabolas shape, then I explained how it is able to do so in a different way.
2. Give an example from this assignment where you used mathematical vocabulary to demonstrate your understanding: I used equation, parabolas and function. Knowing their meanings and in what situation using them.
3. Give an example from this assignment where you used formatting to share the information in a clear and organized way: While explaining what each value does I also gave an example of my parabola vs. the parent parabola.