Quadratic Transformations

Front

What is the vertex form of a quadratic function?

Back

f(x) = a(x-h)² + k

Front

How do we transform from y=x² to y=-3x²?

Back

vertical reflection and vertical stretch

Front

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

Back

(-4, -6)

Front

What steps transform the graph y=x² to y=x²+8?

Back

shifted up 8 units

Front

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

Back

shifted right 4 units

Front

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

Back

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

Front

What effect does a negative 'a' value have on the graph of a quadratic function?

Back

It reflects the graph across the x-axis.

Front

How does changing 'h' in the vertex form f(x) = a(x-h)² + k affect the graph?

Back

It shifts the graph horizontally; left if h is positive, right if h is negative.

Front

How does changing 'k' in the vertex form f(x) = a(x-h)² + k affect the graph?

Back

It shifts the graph vertically; up if k is positive, down if k is negative.

Front

What is the axis of symmetry for the quadratic function in vertex form f(x) = a(x-h)² + k?

Back

x = h