Transformations Of Quadratics

Front

What is a transformation in the context of quadratic functions?

Back

A transformation refers to any change made to the graph of a function, including shifts, reflections, stretches, and compressions.

Front

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

Back

Reflecting a graph across the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

How does multiplying a quadratic function by a negative number affect its graph?

Back

Multiplying a quadratic function by a negative number reflects the graph across the x-axis.

Front

What is the effect of multiplying a quadratic function by a number greater than 1?

Back

Multiplying a quadratic function by a number greater than 1 makes the graph narrower.

Front

What is the effect of multiplying a quadratic function by a number between 0 and 1?

Back

Multiplying a quadratic function by a number between 0 and 1 makes the graph wider.

Front

What does it mean to shift a graph left or right?

Back

Shifting a graph left or right involves adding or subtracting a value from the x-variable in the function.

Front

What does it mean to shift a graph up or down?

Back

Shifting a graph up or down involves adding or subtracting a value from the entire function.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you write the equation of a quadratic function that is reflected across the x-axis and shifted up 3 units?

Back

The equation would be y = -x² + 3.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is given by y = ax² + bx + c.