# Exploring quadratic functions

- Author:
- Callum Marshall

- Topic:
- Functions, Quadratic Functions

## Question 1

Set the values

*and***p***so that the vertex of the black parabola sits on the Origin. i. What is the equation of the black parabola? ii. Move the black parabola so that it lies on top of the red one.***q**iii. What were the values for

*and***p***that you used to move the black parabola on top of the red one? iv. What is the equation of the red parabola? v. Use the input bar to check your answers.***q**## Question 2

Again, set the values

*and***p***so that the vertex of the black parabola sits on the Origin. The equation of the black parabola should now be the same as it was at the start of Qu 1. i. Move the black parabola so that it lies on top of the blue one.***q**ii. What were the values for

*and***p***that you used to move the black parabola on top of the blue one? iii. What is the equation of the blue parabola? iv. Use the input bar to check your solutions.***q**## Question 3

Re-set the values

*and***p***so that the vertex of the black parabola sits on the Origin. i. Move the black parabola so that it lies on top of the green one.***q**i. What were the values for

*and***p***that you used to move the black parabola on top of the green one? ii. What is the equation of the green parabola?***q**## Question 4

Set the values

*and***p***so that the vertex of the black parabola sits on the Origin. i. Find the equation of the black parabola. ii. Move the black parabola so that it lies on top of the blue one.***q**i. What were the values for

*and***p***that you used to move the black parabola on top of the blue one? ii. What is the equation of the blue parabola?***q**## Question 5

Re-set the values

*and***p***so that the vertex of the black parabola sits on the Origin. i. What is the equation of the black parabola? ii. Move the black parabola so that it lies on top of the orange one.***q**i. What were the values for

*and***p***that you used to move the black parabola on top of the orange one? ii. What is the equation of the orange parabola?***q**## Question 6

i. Find the equation of the black parabola.

The black parabola is transformed so that it lies on top of the pink parabola.
ii. Explain HOW the black parabola can be transformed to the pink one.
iii. What is the equation of the pink parabola?

## Question 7

i. Find the equation of the black parabola.

The black parabola is transformed so that it lies on top of the purple parabola.
ii. Explain HOW the black parabola can be transformed to the purple one.
iii. What is the equation of the purple parabola?