7A, 7C Quadratic Attributes and Transformations

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does the vertex of a quadratic function represent?

Back

The vertex of a quadratic function represents the maximum or minimum point of the graph, depending on whether it opens upwards or downwards.

Front

How can you determine if a quadratic opens upwards or downwards?

Back

A quadratic opens upwards if the leading coefficient (a) is positive and downwards if it is negative.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

What is the range of a quadratic function that opens upwards?

Back

The range is all real numbers greater than or equal to the y-coordinate of the vertex.

Front

What is the range of a quadratic function that opens downwards?

Back

The range is all real numbers less than or equal to the y-coordinate of the vertex.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph crosses the x-axis, found by solving the equation f(x) = 0.

Front

What does it mean for a quadratic to be vertically stretched?

Back

A quadratic is vertically stretched when the absolute value of the leading coefficient (a) is greater than 1, making the parabola narrower.

Front

What does it mean for a quadratic to be vertically compressed?

Back

A quadratic is vertically compressed when the absolute value of the leading coefficient (a) is less than 1, making the parabola wider.

Front

What is a transformation in the context of quadratic functions?

Back

A transformation refers to changes made to the graph of a function, such as translations, stretches, or reflections.