Parabola Basics

Front

What is a parabola?

Back

A parabola is a U-shaped curve that is the graph of a quadratic function. It can open upwards or downwards.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does the coefficient 'a' in a quadratic function determine?

Back

The coefficient 'a' determines the direction of the parabola's opening: if 'a' is positive, it opens upwards; if 'a' is negative, it opens 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 x back into the function 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 at 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 f(0).

Front

What is the significance of the vertex in a parabola?

Back

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

Front

How do you determine if a point is the vertex of a parabola?

Back

A point is the vertex if it is the minimum or maximum point of the parabola, which can be confirmed by analyzing the graph.

Front

What is the focal point of a parabola?

Back

The focal point is a specific point inside the parabola where all the reflected rays converge, located along the axis of symmetry.

Front

What is the line of symmetry for the parabola y = ax² + bx + c?

Back

The line of symmetry is given by the equation x = -b/(2a).