Quadratic Transformations

Front

What is a quadratic function?

Back

Front

What does it mean for a quadratic function to be 'narrower' or 'wider'?

Back

A quadratic function is 'narrower' when the absolute value of the leading coefficient (a) is greater than 1, and 'wider' when it is between 0 and 1.

Front

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

Back

The value of 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width (narrower for |a| > 1, wider for 0 < |a| < 1).

Front

What is the vertex of a quadratic function?

Back

Front

What does it mean to reflect a quadratic function over the x-axis?

Back

Reflecting a quadratic function over the x-axis means changing the sign of the leading coefficient 'a', resulting in a downward-opening parabola if it was originally upward-opening.

Front

What is the effect of translating a quadratic function up or down?

Back

Translating a quadratic function up or down involves adding or subtracting a constant from the function, changing the y-coordinate of the vertex.

Front

How do you stretch or compress a quadratic function vertically?

Back

To stretch or compress a quadratic function vertically, multiply the function by a constant factor. If the factor is greater than 1, it stretches; if between 0 and 1, it compresses.

Front

What is the standard form of a quadratic function?

Back

Front

What is the axis of symmetry in a quadratic function?

Back

Front

What does it mean for a quadratic function to have real roots?

Back

A quadratic function has real roots if its graph intersects the x-axis, which occurs when the discriminant (b^2 - 4ac) is greater than or equal to zero.