Quadratic Transformations

Front

What is the axis of symmetry in a function?

Back

A vertical line that passes through the vertex and divides the parabola in half.

Front

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

Back

x = 1.

Front

What does the quadratic function that has a vertex of (3,4) look like?

Back

y = a(x-3)² + 4.

Front

In the vertex form f(x) = a(x - h)² + k, what does the 'h' value do?

Back

Shifts the function left or right.

Front

What steps 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, where (h,k) is the vertex.

Front

What does the 'a' value in the vertex form indicate?

Back

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

Front

How do you find the vertex of a quadratic function in standard form?

Back

Use the formula h = -b/(2a) to find the x-coordinate, then substitute h back into the function to find k.

Front

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

Back

It reflects the graph over the x-axis.

Front

What does shifting a quadratic function up or down involve?

Back

Adding or subtracting a constant from the k value in the vertex form.