Transformations of Parabolas

The video tutorial explains non-rigid transformations, focusing on vertical and horizontal stretches and shrinks. It differentiates these from rigid transformations, which only move graphs without altering their shape. The tutorial provides examples using quadratic functions, demonstrating how multiplying by constants affects the graph's shape. Vertical transformations involve multiplying the entire function, while horizontal transformations involve multiplying inside the function. The video emphasizes understanding the placement of the multiplier to determine the type of transformation.

What is a non-rigid transformation?

• A transformation that reflects the graph.

• A transformation that rotates the graph.

• A transformation that only moves the graph without changing its shape.

• A transformation that changes the shape of the graph.

What causes a vertical stretch in a function?

• Multiplying the function by a constant greater than 1.

• Subtracting a constant from the function.

• Adding a constant to the function.

• Multiplying the function by a constant less than 1.

In the example of vertical stretch, what happens to the parabola when the function is multiplied by 4?

• The parabola shifts to the left.

• The parabola becomes wider.

• The parabola shifts to the right.

• The parabola becomes narrower.

What is a vertical shrink?

• A transformation that shifts the graph upwards.

• A transformation that makes the graph shorter.

• A transformation that shifts the graph downwards.

• A transformation that makes the graph taller.

In the example of vertical shrink, what happens to the parabola when the function is multiplied by 1/2?

• The parabola becomes narrower.

• The parabola becomes wider.

• The parabola shifts to the right.

• The parabola shifts to the left.

What causes a horizontal shrink in a function?

• Multiplying the inside of the function by a constant greater than 1.

• Multiplying the inside of the function by a constant less than 1.

• Adding a constant to the function.

• Subtracting a constant from the function.

In the example of horizontal shrink, what happens to the parabola when the inside of the function is multiplied by 4?

• The parabola becomes wider.

• The parabola shifts to the left.

• The parabola becomes narrower.

• The parabola shifts to the right.

What causes a horizontal stretch in a function?

• Adding a constant to the function.

• Subtracting a constant from the function.

• Multiplying the inside of the function by a constant less than 1.

• Multiplying the inside of the function by a constant greater than 1.

In the example of horizontal stretch, what happens to the parabola when the inside of the function is multiplied by 1/4?

• The parabola becomes wider.

• The parabola shifts to the left.

• The parabola becomes narrower.

• The parabola shifts to the right.

What is the key difference between vertical and horizontal transformations?

• Both affect the y-values.

• Both affect the x-values.

• Vertical transformations affect the y-values, while horizontal transformations affect the x-values.

• Vertical transformations affect the x-values, while horizontal transformations affect the y-values.