Attributes of Parabolas

Front

What is the axis of symmetry of a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. For a parabola in the form y = ax^2 + bx + c, the axis of symmetry can be found using the formula x = -b/(2a).

Front

What does it mean when a parabola opens downward?

Back

When a parabola opens downward, it indicates that the coefficient 'a' in the quadratic equation is negative. This means the vertex of the parabola is a maximum point.

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 upward or downward. It can be found using the formula x = -b/(2a) and substituting back to find the y-coordinate.

Front

How can you determine if a parabola opens up or down?

Back

You can determine the direction by looking at the coefficient 'a' in the quadratic equation y = ax^2 + bx + c. If 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.

Front

What is the significance of the vertex in a parabola?

Back

The vertex represents the maximum or minimum value of the quadratic function, and it is the point where the parabola changes direction.

Front

What is the formula to find the vertex of a parabola given in standard form?

Back

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

Front

What does the term 'maximum' refer to in the context of parabolas?

Back

A maximum refers to the highest point on a downward-opening parabola, which is the vertex.

Front

What does the term 'minimum' refer to in the context of parabolas?

Back

A minimum refers to the lowest point on an upward-opening parabola, which is the vertex.

Front

What is the relationship between the axis of symmetry and the vertex?

Back

The axis of symmetry passes through the vertex of the parabola, dividing it into two equal halves.

Front

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

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) in the equation y = ax^2 + bx + c.