Transformation of Curves By: James Wu

Task A: Straight Lines

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

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

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).

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

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

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

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

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

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.

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.