WU: Characteristics of Parabolas

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, dividing it into two mirror-image halves.

Front

How is the vertex of a parabola defined?

Back

The vertex is the highest or lowest point of a parabola, depending on its orientation (opening upwards or downwards).

Front

What are the coordinates of the vertex in the parabola represented by the equation y = (x - 4)² - 4?

Back

The vertex is at the point (4, -4).

Front

What is the range of a parabola that opens upwards?

Back

The range is all values of y that are greater than or equal to the y-coordinate of the vertex.

Front

What is the domain of a parabola?

Back

The domain of a parabola is all real numbers, as parabolas extend infinitely in the horizontal direction.

Front

What is the standard form of a quadratic equation representing a parabola?

Back

The standard form is y = ax² + bx + c, where a, b, and c are constants.

Front

What does the value of 'a' in the quadratic equation y = ax² + bx + c indicate about the parabola?

Back

The value of 'a' determines the direction of the parabola's opening: if 'a' is positive, it opens upwards; if 'a' is negative, it opens downwards.

Front

How can you find the x-coordinate of the vertex from the standard form of a quadratic equation?

Back

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

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, which occurs when x = 0.

Front

What is the effect of changing the value of 'b' in the quadratic equation on the parabola's graph?

Back

Changing the value of 'b' affects the position of the vertex and the axis of symmetry, but does not change the direction of the parabola's opening.