Key Features of Parabolas

Front

What is a parabola?

Back

A parabola is a symmetrical, U-shaped curve that represents the graph of a quadratic function. It can open upwards or downwards depending on the coefficient of the x² term.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you find the vertex of a parabola given in standard form?

Back

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

Front

What is the axis of symmetry in 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).

Front

What is the y-intercept of a parabola?

Back

The y-intercept is the point where the parabola crosses the y-axis, found by evaluating the function at x = 0.

Front

What is the domain of all quadratic functions?

Back

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

Front

What is the range of a parabola that opens upwards?

Back

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

Front

What is the range of a parabola that opens downwards?

Back

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

Front

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

Back

A parabola opens upwards if the coefficient 'a' in the equation y = ax² + bx + c is positive, and it opens downwards if 'a' is negative.