Quadratic Functions: Vertex and Axis of Symmetry

Front

Which letter determines if a parabola opens up or down?

Back

The letter 'a' in the quadratic function y = ax^2 + bx + c determines the direction of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the vertex of the parabola represented by the function y = -2(x + 2)^2 + 1?

Back

The vertex of the parabola is (-2, 1). This is found from the vertex form of a quadratic function, y = a(x - h)^2 + k, where (h, k) is the vertex.

Front

The ________ is the highest or lowest part of a graph.

Back

The vertex is the highest or lowest point of a parabola, depending on whether it opens upwards or downwards.

Front

The lowest point on a parabola is called the ______.

Back

The lowest point on a parabola is called the minimum.

Front

What is the axis of symmetry for the parabola represented by the function y = 3(x - 2)^2 + 4?

Back

The axis of symmetry is x = 2, which is the x-coordinate of the vertex.

Front

In the quadratic function y = ax^2 + bx + c, what does 'b' represent?

Back

The 'b' in the quadratic function affects the position of the vertex along the x-axis and influences the axis of symmetry.

Front

What is the formula to find the vertex of a parabola given in standard form y = ax^2 + bx + c?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting it back into the function to find the y-coordinate.

Front

If a parabola opens downwards, what can be said about its vertex?

Back

If a parabola opens downwards, its vertex is the maximum point of the graph.

Front

What is the significance of the 'k' value in the vertex form of a quadratic function?

Back

In the vertex form y = a(x - h)^2 + k, the 'k' value represents the y-coordinate of the vertex.

Front

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

Back

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