Quadratics #4 Review

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, represented as (-infinity, infinity).

Front

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

Back

The range is from the vertex's y-coordinate to infinity, represented as [k, infinity) where k is the vertex's y-coordinate.

Front

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

Back

The range is from negative infinity to the vertex's y-coordinate, represented as (-infinity, k] where k is the vertex's y-coordinate.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, given by the equation x = h, where (h,k) is the vertex.

Front

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

Back

A parabola opens upwards if the coefficient 'a' in the equation y = ax^2 + bx + c is positive, and downwards if 'a' is negative.

Front

What does it mean for a quadratic function to have a maximum value?

Back

A quadratic function has a maximum value if it opens downwards, meaning the vertex represents the highest point on the graph.

Front

What does it mean for a quadratic function to have a minimum value?

Back

A quadratic function has a minimum value if it opens upwards, meaning the vertex represents the lowest point on the graph.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) for the x-coordinate, and then substituting back to find the y-coordinate.

Front

What is the significance of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola (up or down) and affects the width of the parabola.