The variables a, h, and k have specific meanings and play a crucial role in shaping the parabola.

The value of “a” determines the direction and width of the parabola. In this equation, a is -1/2, which means the parabola opens downwards since “a” is negative. Compared to its parent function (y=x^2), this parabola has a negative coefficient (-1/2) in front of the squared term, so This causes the parabola to be wider than the parent function, due to the “a” that is in between 0 and -1. The width of the parabola is stretched horizontally, resulting in a wider shape.

The value of “h” represents the horizontal shift of the parabola. In this equation, h is 3, indicating that the vertex of the parabola is horizontally shifted 3 units to the right compared to the parent function. It determines the new position of the vertex along the x-axis.

The value of “k” represents the vertical shift of the parabola. In this equation, k is -4, indicating that the vertex of the parabola is vertically shifted 4 units downward compared to the parent function. It determines the new position of the vertex along the y-axis.

Self-Assessment

In this assignment, I represented the same mathematical idea in multiple ways by expressing the equation of a parabola in different forms. The given equation y = -1/2(x-3)^2 – 4 is written in vertex form, which shows the vertex of the parabola at (3, -4) and the coefficient -1/2 indicating that the parabola opens downwards.

The relevant mathematical vocabulary words used to demonstrate understanding include:

– Equation: A statement that two expressions are equal.

– Parabola: A U-shaped curve formed by a quadratic function.

– Vertex: It shows the point where the parabola begins to open.

– Coefficient: A numerical factor multiplying a variable.

To share this information in a clear and organized way, I used bullet points to separate each question and provided numbered responses for each question, also in the Desmos I changed the settings to make it more clear. This formatting helps to visually organize the information and make it easier to read and understand.

The first time that I tried this problem I found it challenging because I did not know what should I do with the bracket.

The first time that I tried it, I squared everything inside of the brackets.

The strategies that I used to figure it out were: 1- I asked for help from my teacher. 2- I listened carefully to all my teacher’s explanations and tried to learn the solution. 3- I watched YouTube videos about this kind of problem, and I did some problems like this problem, in order to remember everything completely.

The skill that I used to solve this problem correctly was: foiling the squared binomial and combining like terms to solve the rest of the problem.

Next time I encounter a difficult problem, I might use the same strategies to figure out future problems.