Quadratics Transformations in Vertex Form

Front

What is the vertex form of a quadratic function?

Back

f(x) = a(x-h)² + k

Front

What is the name of the imaginary line that cuts a parabola in half and goes through the vertex?

Back

Axis of symmetry

Front

If the blue graph is f(x) = x², what is the red graph if it is shifted down by 5 units?

Back

g(x) = x² - 5

Front

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

Back

x = 1

Front

Identify the vertex of f(x) = -2(x+1)² + 3.

Back

(-1, 3)

Front

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

Back

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

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

Back

It reflects the graph across the x-axis.

Front

What is the vertex of the function f(x) = 3(x-2)² - 4?

Back

(2, -4)