Quadratic Transformations

Front

What is the vertex of the equation y = (x + 4)² - 6?

Back

(-4, -6)

Front

Describe the transformation of f(x) = (x + 7)² compared to the parent function.

Back

horizontal shift left 7 units

Front

What steps transform the graph y = x² to y = (x - 4)²?

Back

Shifted right 4 units

Front

What is the vertex form of a quadratic function?

Back

f(x) = a(x - h)² + k

Front

Which equation matches the transformation: up 4, stretched 3, reflected down, and left 1?

Back

f(x) = -3(x + 1)² + 4

Front

What does the 'a' in the vertex form f(x) = a(x - h)² + k represent?

Back

The vertical stretch or compression factor and the direction of the parabola (upward if a > 0, downward if a < 0).

Front

What is the effect of a positive 'k' in the vertex form of a quadratic function?

Back

It shifts the graph vertically upwards by 'k' units.

Front

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

Back

It shifts the graph horizontally to the left by 'h' units.

Front

How does the graph of y = -x² compare to y = x²?

Back

It is reflected over the x-axis.

Front

What transformation occurs when the equation is changed from y = x² to y = x² + 3?

Back

The graph shifts vertically up 3 units.