Equations
Red: f(x)=x^2
Green: f(x)=(x-8)^2+3
Blue: f(x)=-1/3(x-5)^2
Purple: f(x)=3(x+8)^2-4
Black: f(x)=1/8(x-11)^2-2
Paragraph
In my green equation, I had h=8 (appearing in the equation as a negative 8) which moved the axis of symmetry 8 places to the right. In that same equation, k=3 which moved the vertex up by 3 spots. In my blue equation, the same rules applied for h as they did in the green equation, but this equation had a=-1/3 which set the parabola facing down due to it being negative. Because a was over 0 and less than 1, this caused the parabola to be less narrow than the others. In the purple equation, h was instead a negative number, appearing positive in the equation. This moved the axis of symmetry to the left instead. a was over 1, which made the parabola much slimmer instead. k was a negative number, making the vertex below the x-axis by 4. In the black equation, a was equal to 1/8. This made the parabola much wider than the other ones. This proved that the smaller the fraction, the wider it would be.
Self-Assessment
- I presented the same mathematical equation in different ways by either excluding different variables, making them negative/positive, and by changing the numbers of the variables.
- I used vocabulary words such as vertex, parabola, and axis of symmetry. The vertex is the point where the parabola begins, a parabola is a symmetrical curve which is made using a quadratic equation, and the axis of symmetry is a line down x-axis where the parabola is split in half and is symmetrical on each side. I used these words from memory.
- I made formatting easy and clear to read by making sure to not overlap parabolas by much, and by making sure the vertex labels were out of the way from other lines. I made sure that the lines, points, and labels were all colour coded as to not be confusing.