Parabola Basics Math I Flashcard Fall 24

Front

What is a parabola?

Back

A parabola is a U-shaped curve that is defined as the set of all points that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the parabola, depending on its orientation. It is the point where the parabola changes direction.

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it has a minimum point at its vertex and the arms of the parabola extend upwards.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it has a maximum point at its vertex and the arms of the parabola extend downwards.

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 passes through the vertex.

Front

How do you find the y-intercept of a parabola?

Back

The y-intercept is found by setting x = 0 in the equation of the parabola and solving for y.

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 coefficient 'a' in the quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the formula for finding the vertex of a parabola in standard form?

Back

The vertex (h, k) can be found using the formula h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

Front

What is the line of symmetry for the parabola y = ax^2 + bx + c?

Back

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