Parabola in Orange: y = ½ (x – 7)2 – 1 ( in the form of y = a(x – h)2 + k )
Standard Parabola in blue: y = x2
What makes the parabola (in orange) different from the standard parabola (in blue)?
- Value of ‘a‘: First, because a is greater than zero (a positive value), it opens upwards. The shape is wider than the standard parabola because a is a fraction, which is less than 1. The lesser the a value, the wider the parabola.
- Value of ‘h‘: When a value (h) is subtracted from x (x – h), it shifts the parabola and the vertex to the right side. In this case, it shifted to the right by 7 because 7 was subtracted from the x (x – 7). The axis of symmetry is also 7 because x = 7.
- Value of ‘k‘: The k value can shift a parabola vertically. If the k value is positive, it is shifted up, but if it is negative, then it is shifted down. For this parabola, it is shifted down by 1, because the value of k is -1. This can determine the minimum value, which is y = -1, as the range of the parabola is greater than or equal to -1.
Self-Assessment
1. Give an example from this assignment where you represented the same mathematical idea in three different ways.
First, the parabolas are presented in the form of a written equation. The equation is then formatted into a visual graph using Desmos. The equation was then broken down and explained in further detail in sentences.
2. Give an example from this assignment where you used mathematical vocabulary to demonstrate your understanding.
An example from the assignment is “[a value] shifts the parabola and the vertex to the right side”. I used words like “shift” and “vertex” to describe a parabola.
3. Give an example from this assignment where you used formatting to share the information in a clear and organized way.
I first used two colours to differentiate the parabolas and the equations for them. The sentences were then formatted into a linear/list form to clearly present all the ideas. I also colour coded parts of the parabola.