Exploring Quadratic Transformations

ax + b

ax^2 + bx

x^2 + bx + c

ax^2 + bx + c

The y-intercept

The focus

The x-intercept

The vertex

Division inside the function

Subtraction inside the function

Addition inside the function

Multiplication inside the function

Horizontal stretch

Horizontal shift

Vertical stretch

Reflection over the x-axis

Dividing the x variable inside the function

Subtracting from the x variable inside the function

Multiplying the x variable inside the function

Adding to the x variable inside the function

Division of the function outside the brackets

Multiplication of the function outside the brackets

Subtraction from the function outside the brackets

Addition to the function outside the brackets

Doubles the x-values of the points

Halves the y-values of the points

No change to the points

Doubles the y-values of the points

The slope of the parabola

The maximum value of the function

The intercepts of the parabola

The vertex of the parabola

The parabola is narrower than usual

The parabola is wider than usual

The parabola opens downwards

The parabola opens upwards

It shifts to the right

It flips over the y-axis

It shifts to the left

It becomes narrower