Quadratic transformations

Front

What are the steps to transform the graph y = x² to y = 2(x+2)² - 5?

Back

Stretch by 2, shifted 2 units left and 5 down.

Front

What is the vertex form of a quadratic function?

Back

f(x) = a(x-h)² + k.

Front

What is the axis of symmetry in the function f(x) = (x-1)² + 2?

Back

x = 1.

Front

What does the equation y = -3(x-2)² + 1 describe?

Back

Reflected over x and stretched by 3.

Front

How do we transform the parent function f(x) = x² to f(x) = -x²?

Back

Reflection over the x-axis.

Front

What is the effect of the coefficient 'a' in the vertex form f(x) = a(x-h)² + k?

Back

It determines the vertical stretch or compression and the direction of the parabola.

Front

What does the term (x-h) represent in the vertex form of a quadratic function?

Back

It represents a horizontal shift of the graph h units to the right.

Front

What does the term k represent in the vertex form of a quadratic function?

Back

It represents a vertical shift of the graph k units up or down.

Front

How do you find the vertex of the quadratic function f(x) = 2(x+3)² - 4?

Back

The vertex is at (-3, -4).

Front

What is the effect of a negative 'a' value in the vertex form of a quadratic function?

Back

It reflects the graph over the x-axis.