What is a parabola?
A parabola is most commonly known as a U-shaped line developed when graphing a quadratic function in the form of f(x)=a(x-h)^2+k.
The significance of the variables a, h, and k.
A determines the width of a parabola, as well as whether the parabola is downturned or upturned. If A=0<_<+/-1 (1/2, -3/4, etc.), the parabola will be wider, and if A=0<_>+/-1(2,-5, etc.), the parabola will be narrower. To determine whether a parabola is upturned or downturned depends on the value of A. If A is a negative number, the parabola will be downturned, and if A is a positive number, the parabola will be upturned.
H is the X value of the vertex of a parabola. The parabola’s line of symmetry is shown when X=H. the line of symmetry is the point where you can vertically split the graph in two and have perfectly symmetrical halves.
K is the Y value of the vertex of a parabola. The vertex is the highest or lowest point of the parabola, which is where the parabola starts to curve.
Significance of a, h, and k in my equation.
My equation: f(x)=-1/2(x-3)^2-4 (red line). Standard equation: f(x)=x^2 (green line)
In my equation the A value is a negative number, as well as a fraction which is a number smaller than zero. This means my parabola will be wider, and downturned, unlike the standard equation which is narrower and upturned. The vertex of my parabola is (3,-4). I know this because my H value is 3, and my K value is -4. This differs from the standard equations vertex which is (0,0). My parabola’s axis of symmetry is X=3, because that is the point where one can cut my parabola in half and have symmetrical sides. Meanwhile, the standard equations axis of symmetry is X=0.
Self assessment
- I represented the same mathematical equation visually, in writing, and in equation form. Using the equation given, I input it into Desmos, giving me a graph form of that equation, then I wrote about the significance of a, h, and k in said equation and how that determines the visual appearance of my parabola.
- An example of where I used mathematical vocabulary to show my understanding was when I was explaining the significance of a, h, k in my equation. I used vocab like negative number, vertex, fraction, axis of symmetry, symmetrical, and equation.
- An example of me using formatting to make my post more clear and understandable was the colour coding of a, h, and k, as well as their explanations. this makes the information more visible, and easier to find.