Quadratic Graphs & Characteristics

Front

What is the domain of a quadratic function?

Back

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

Front

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

Back

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

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 parabola?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the quadratic equation y = ax^2 + bx + c.

Front

What does it mean for a parabola to open upwards?

Back

A parabola opens upwards if the coefficient of x^2 (a) is positive.

Front

What does it mean for a parabola to open downwards?

Back

A parabola opens downwards if the coefficient of x^2 (a) is negative.

Front

How do you determine the range of a quadratic function that opens downwards?

Back

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

Front

What is the standard form of a quadratic function?

Back

The standard form is y = ax^2 + bx + c.

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.

Front

How can you identify the vertex from the standard form of a quadratic function?

Back

You can find the vertex using the formula h = -b/(2a) and k = f(h).