Red
The equation f(x) = x2 can be transformed into the general form of a quadratic function, which is: f(x) = a(x-h)2+k. In this equation, the vertex is (0,0) which means the axis of symmetry is right at point 0, with a minimum value of 0. Since both the h and k value are zero, the graph will neither have a vertical or a horizontal stretch.
Black
The equation f(x) = -1/2(x-2)2+3 can be transformed into the general form of a quadratic function, which is: f(x) = a(x-h)2+k. In this equation, the vertex is (2,3) which means the axis of symmetry is right at point 2. The h value of 2 shifts the graph 2 units to the right, and the k value of 3 shifts the graph 3 units up. The coefficient a is -1/2, which reflects the graph over the x-axis, causing it to open downwards, and compresses it vertically, making it wider. Together, these transformations result in a downward-opening, wider parabola with a maximum value of 3.
Green
The equation f(x) = -2(x-4)2 +3 can be written in the general form of a quadratic function, f(x) = a(x-h)2+k. In this case, the vertex is at (4,3), meaning the axis of symmetry is at x = 4. The h value of 4 shifts the graph 4 units to the right, and the k value of 3 shifts the graph 3 units up. The coefficient a is −2, which reflects the graph over the x-axis, making it open downwards, and stretches it vertically, making it steeper. These transformations result in a downward-opening, narrower-shaped parabola with a maximum value of 3.
Orange
The equation f(x) = 2(x+3)2+1 can be written in the general form of a quadratic function, f(x) = a(x-h)2+k. Here, the vertex is at (-3,1), meaning the axis of symmetry is at x = -3. The h value of -3 shifts the graph 3 units to the left, and the k value of 1 shifts the graph 1 unit up. The coefficient a is 2, which reflects the graph over the x-axis, making it open upwards, and stretches it vertically, making it steeper. These transformations result in an upwards-opening, narrower shaped parabola, with a minimum value of 1.
Purple
The equation f(x) = 1/4(x+1)2 can be written in the general form of a quadratic function, f(x) = a(x-h)2+k. In this case, the vertex is at (−1,0), meaning the axis of symmetry is at x=−1. The h value of −1 shifts the graph 1 unit to the left, and the k value of 0 means there is no vertical shift. The coefficient a is 1/4, which reflects the graph over the x-axis, making it open upwards, and compresses it vertically, making it wider. These transformations produce an upwards-opening, wider parabola, with a minimum value of 0.
Self-Assessment
1. How did you represent the same mathematical idea in multiple ways in this assignment?
I used Desmos to visually showcase my quadratic functions, giving readers a clear vision while reading my explanation for “a”, “h”, and “k” and how the transformations affected the graph.
2. State some of the relevant mathematical vocabulary words you used to demonstrate your understanding and their definitions. State where you found the definitions (your own memory, class notes, online?)
I used mathematical vocabulary such as “positive”, “negative”, “shift”, “horizontally”, “vertically”, “quadratic”, “function”, “vertex”, “axis of symmetry”, “minimum value” and “maximum value”. I got the definitions from class memories and online class notes.
3. How did you use formatting to share your information in a clear and organized way?
I used the same formatting to explain the transformations for all five quadratic equations so readers could get a better understanding.