Key Features of Quadratic Graphs

Front

What is the axis of symmetry of a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a) for a quadratic equation in the form y = ax^2 + bx + c.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula (h, k) where h = -b/(2a) and k is the value of the quadratic function at h.

Front

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

Back

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

Front

What does it mean for a parabola to be concave up?

Back

A parabola is concave up when it opens upwards, resembling a 'U' shape. This indicates that the vertex is the minimum point of the graph.

Front

What does it mean for a parabola to be concave down?

Back

A parabola is concave down when it opens downwards, resembling an 'n' shape. This indicates that the vertex is the maximum point of the graph.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants.

Front

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

Back

The 'a' value determines the direction of the parabola (upward or downward) and affects the width of the parabola. A larger absolute value of 'a' results in a narrower parabola.

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, represented as (-∞, ∞). This means that any real number can be input into the function.

Front

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

Back

The range of a quadratic function that opens upwards is [k, ∞), where k is the y-coordinate of the vertex.

Front

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

Back

The range of a quadratic function that opens downwards is (-∞, k], where k is the y-coordinate of the vertex.