Quadratic Transformations

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants.

Front

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

Back

A negative 'a' value reflects the parabola across the x-axis.

Front

How does changing the 'a' value in the equation y = ax^2 affect the width of the parabola?

Back

Increasing the absolute value of 'a' makes the parabola narrower, while decreasing it makes the parabola wider.

Front

What does it mean to compress a parabola vertically?

Back

To compress a parabola vertically means to multiply the 'a' value by a fraction (0 < k < 1), making it wider.

Front

What does it mean to stretch a parabola vertically?

Back

To stretch a parabola vertically means to multiply the 'a' value by a number greater than 1, making it narrower.

Front

How do you represent a parabola that has been moved 'h' units to the right?

Back

A parabola moved 'h' units to the right is represented as y = a(x - h)^2 + k.

Front

How do you represent a parabola that has been moved 'k' units up?

Back

A parabola moved 'k' units up is represented as y = ax^2 + k.

Front

What is the effect of moving a parabola to the left?

Back

Moving a parabola to the left by 'h' units is represented as y = a(x + h)^2 + k.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Front

What does it mean to reflect a parabola across the x-axis?

Back

Reflecting a parabola across the x-axis means changing the sign of 'a' in the equation y = ax^2.