My equation: 𝑦=2(𝑥−4)2+2
The parent function: y=x2
Comparing the Two Functions on the Same Graph
As you can see, the red parabola is narrower, shifted to right by 4 and the minimum is at 2. The parent function is wider, centered on the y axis and has a minimum of 0.
The significance of a, h, and k in the parabola 𝑦=2(𝑥−4)2+2. Formula: y=a(x-h)+k
The significance of a is that it determines how narrow or wide the graph is, alongside whether it is upwards or down on the y-axis. Since the a value of my parabola equation is 2, the parabola is a narrow, upwards graph. If it were to be 1 or even a fraction, it would be wider. A positive a value causes a graph to be upwards and a negative a value causes the parabola to be downwards. The value of h determines if the graph is on the right or on the left of the x-axis. When an h value is plugged into the formula, the sign switches. So a positive h value receives a negative sign but a negative h value receives a positive sign. In short, if the h value appears negative, it is actually positive. Same with the an h value appearing positive, (the number itself is negative). Therefore, when an h value is observed, the opposite can be inferred. H values appearing to be negative is on the right side of the x axis because the actual number is positive. H values appearing to be positive in on the left of the x axis because the actual number is negative. The h value is the x coordinate of the vertex. Lastly, the k value is the y coordinate of the vertex. It determines where the minimum or the maximum of the parabola is on the y coordinate. The k value also determines the range of the parabola. Adding a k value greater or less than 0 shifts the parabola up or down (up: positive k; down: negative k). The a and k values do interact with each other. If the a value is negative than the k value determines a “maximum” value. If the a value is positive, the k value represents a “minimum” value. Therefore the a affects the width and direction on the y axis of the parabola, the h value affects the placement of the parabola on the x axis and the k value decides where vertex of the parabola on the y axis is.
Communication Core Competency
I represented the same mathematical idea through the paragraph above, my equation and the graph of my equation
I used the following mathematical terms: minimum, maximum, x-axis, y-axis, positive, negative, coordinate, vertex, parabola and formula.
For formatting I included headings to describe what the section was highlighting regarding parabolas. I also ensured that my parabola and the parent function were separate colours for clarity.