Characteristics of Parabolas

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 determines if a parabola opens up or down?

Back

The direction in which a parabola opens is determined by the coefficient of the quadratic term (a) in the equation y = ax^2 + bx + c. If a > 0, it opens up; if a < 0, it opens down.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens down or up.

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, passing through the vertex.

Front

How do you find the vertex of a parabola given its equation?

Back

For the equation y = ax^2 + bx + c, the vertex can be found using the formula x = -b/(2a) and then substituting x back into the equation to find y.

Front

What is the maximum value of a parabola?

Back

The maximum value occurs at the vertex of a downward-opening parabola.

Front

What is the minimum value of a parabola?

Back

The minimum value occurs at the vertex of an upward-opening parabola.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c.

Front

What is the significance of the y-intercept in a parabola?

Back

The y-intercept is the point where the parabola crosses the y-axis, found by setting x = 0 in the equation.

Front

How can you determine if a parabola has a maximum or minimum?

Back

If the coefficient 'a' in the quadratic equation is negative, the parabola has a maximum; if 'a' is positive, it has a minimum.