Quadratic Transformations

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x².

Front

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

Back

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

Front

How does a positive 'k' value affect the graph of a quadratic function?

Back

A positive 'k' value shifts the graph vertically upwards.

Front

How does a negative 'k' value affect the graph of a quadratic function?

Back

A negative 'k' value shifts the graph vertically downwards.

Front

What transformation occurs when the equation is changed from f(x) = x² to f(x) = (x + 3)²?

Back

The graph shifts horizontally left by 3 units.

Front

What transformation occurs when the equation is changed from f(x) = x² to f(x) = (x - 5)²?

Back

The graph shifts horizontally right by 5 units.

Front

What does it mean to vertically stretch a quadratic function?

Back

Vertically stretching a quadratic function makes it steeper, which occurs when the absolute value of 'a' is greater than 1.

Front

What does it mean to vertically compress a quadratic function?

Back

Vertically compressing a quadratic function makes it less steep, which occurs when the absolute value of 'a' is between 0 and 1.

Front

If f(x) = 2(x - 1)² + 3, what transformations are applied to the parent function?

Back

The graph is vertically stretched by a factor of 2, shifted right 1 unit, and shifted up 3 units.

Front

What is the effect of reflecting a quadratic function over the x-axis?

Back

Reflecting a quadratic function over the x-axis changes the sign of 'a', making the parabola open downwards if it originally opened upwards.