Basic graph:
Opens up and is wider:
Opens down and is more narrow
Shifted to the right of the parent function:
shifted down lower than the parent function:
The a,h, and k in Parabola equations are values that determine the shape, location, and size, of the parabola. the full equation of a parabola is x=a(x-h)^2+k. The k indicates the location of the parabola amount the y axis like in the black parabola. With a negative k, the curve is shifted down and vice versa, a positive k will shift the parabola up. The h, meanwhile, shifts the parabola via the x-axis, like the purple curve. With a negative h, it is shifted to the right, while a positive h will do the opposite, to the left. This seemingly odd of negative-positive x and positive-negative x is due to the square. The a is to change the width of the opening of the parabola and what side(up/down) the parabola is open to. like the blue curve and green curve in the blue curve, the a is positive, meanwhile in the green curve the a is negative, and that is the factor of which side the parabola opens to. the value of a is the factor that decides how wide the opening is, in the blue curve the a is a fraction, which makes the parabola wider, while in green, it is bigger than 1, which makes the parabola open more narrow.
I represented the same Mathematical idea in this assignment both in written language and visually, an example is provided with the graph with a simple explanation of its variation below with its own unique aspect. It is then later explained what its variation is and what each variable does.
Vertex: The maximum/minimum point on the parabola
maximum: highest point(highest y value) on the graph(sometimes doesn’t exist)
minimum: Lowest point(lowest x value) on the graph(sometimes doesn’t exist)
x-intercept: where the parabola touches the x-axis(y=0)
y-intercept: where the parabola touches the y-axis(x=0)
Parabola: a U-shaped curve
I used formatting to provide a clear example and definition of parabolas, I first used a graph to provide what the parabolas look like, then have each of their equation listed out along with how to vary from the parent function. In the paragraph after that, I explained what and how each variable, a,h and k modifies the parabola.