1. Transformation of Curves
By: James Wu

2. Task A: Straight Lines

3. I notice that when the coefficient of X becomes larger, the line becomes steeper.

4. When you add a constant term to the equation of a straight line, it affects the gradient of the line
More straight lines

5. Y = mx + c
The significance of M within the equation of a straight line is that it signifies the slope of the line. This will determine whether or not the line is positive or negative.
C stands for the y-intercept of the straight line. It shows where the line will cross the y axis of the graph.
The equation of the graph is ‘y=3x-4’. The reason for this is because the slope rise/run = 3. The line also crosses the y-intercept at point (0,-4).

6. Depending on the coefficient of x², the shape of the parabola will change.
When there is a negative sign in front of the x², the parabola becomes inversed.
Task B: Quadratics

7. More quadratics Different constant terms still have the same
effect on the curves as the constant terms
have on straight lines.
‘Y=x²-2’. This is because all curves must be
x² and since the curve passes through the
Y-intercept at the point (0,-2).
More quadratics

8. Quadratics Again These two curves are similar to
each other. This is because the
letter A in the formula
Y=(x-a)² shows us where
the quadratic will inversely meet the x axis.
Quadratics Again

9. Parabolas in Real Life 1) Measuring breaking distance 2) Heaters
3) Satellite Dishes
4) McDonald’s Arches
5) Golden Gate Bridge

10. What is a Cubic?
They all have different gradients, but all other properties remain the same.

11. The generalization that I can make about the curve y=x³+a is that they have the same properties with straight lines and parabolas, the constant term signifies the location of where the cubic shall meet the y-intercept.

12. I predict that the curve y=-x³ will be inverse and shall cross through the y axis at the point (0,0).
The generalization of y=(x-a)³ is similar to quadratics, the term A is inverse
to where the cubic will meet the x axis.