(h&k) Quadratic transformation

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 and a ≠ 0.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation.

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, as there are no restrictions on the x-values.

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 does a horizontal translation of a quadratic function do?

Back

A horizontal translation shifts the graph left or right. For example, g(x) = (x + 4)² shifts the graph of f(x) = x² left by 4 units.

Front

What does a vertical translation of a quadratic function do?

Back

A vertical translation shifts the graph up or down. For example, g(x) = x² + 5 shifts the graph of f(x) = x² up by 5 units.

Front

What effect does a negative sign in front of a quadratic function have?

Back

A negative sign reflects the graph across the x-axis. For example, g(x) = -x² opens downwards.