Key Features 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 upwards or downwards?

Back

The sign of the 'a' value in the quadratic equation y = ax^2 + bx + c. If 'a' is positive, it opens upwards; if negative, it opens downwards.

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 of a parabola?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form of the quadratic equation.

Front

What are x-intercepts of a parabola?

Back

X-intercepts are the points where the parabola crosses the x-axis, found by setting y = 0 in the equation.

Front

What is the significance of the 'b' value in the quadratic equation?

Back

The 'b' value affects the position of the vertex and the axis of symmetry of the parabola.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the difference between maximum and minimum in parabolas?

Back

A maximum is the highest point of a downward-opening parabola, while a minimum is the lowest point of an upward-opening parabola.

Front

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

Back

By examining the sign of the 'a' value: if 'a' is positive, it has a minimum; if negative, it has a maximum.

Front

What is the formula to find the y-coordinate of the vertex?

Back

The y-coordinate of the vertex can be found using the formula y = f(-b/(2a)).