Characteristics of Parabolas

Front

What is a parabola?

Back

A parabola is a U-shaped curve that is the graph of a quadratic function, represented by the equation y = ax² + bx + c.

Front

What does the 'a' value in a quadratic equation determine?

Back

The 'a' value determines the direction in which the parabola opens: if 'a' is positive, it opens upwards; if 'a' is 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 whether it opens up or down.

Front

How do you find the axis of symmetry for a parabola?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the quadratic equation y = ax² + bx + c.

Front

What is the significance of the maximum or minimum value of a parabola?

Back

The maximum or minimum value of a parabola is the y-coordinate of the vertex, indicating the highest or lowest point of the graph.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it has a maximum vertex, meaning the highest point is at the vertex.

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it has a minimum vertex, meaning the lowest point is at the vertex.

Front

How can you determine if a quadratic function has a maximum or minimum?

Back

You can determine this by looking at the 'a' value: if 'a' is positive, it has a minimum; if 'a' is negative, it has a maximum.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

What is the effect of changing the 'b' value in a quadratic equation?

Back

Changing the 'b' value affects the position of the vertex and the axis of symmetry but does not change the direction in which the parabola opens.