Understanding Quadratic Functions in Vertex Form

The video tutorial explains the vertex form of a quadratic function, which is expressed as f(x) = a(x - H)^2 + K. It identifies the vertex as (H, K) and the axis of symmetry as x = H. The direction in which the parabola opens depends on the value of 'a': it opens downwards if 'a' is less than zero and upwards if 'a' is greater than zero. An example is provided with the function f(x) = -(x + 2)^2 - 3, where the vertex is (-2, -3) and the axis of symmetry is x = -2. The video also demonstrates how to graph the function by finding additional points, such as the Y-intercept, to determine the parabola's width and shape.

What is the vertex of a quadratic function in vertex form f(x) = a(x - h) + k?

• -h, k

• h, -k

• h, k

• a, k

Tags

CCSS.HSF-IF.C.7A

If the value of 'a' in the vertex form of a quadratic function is negative, what does this indicate about the parabola?

• The parabola has no vertex.

• The parabola opens downwards.

• The parabola opens upwards.

• The parabola is a straight line.

In the example f(x) = -(x + 2)^2 - 3, what is the axis of symmetry?

• x = 3

• x = -3

• x = 2

• x = -2

Tags

CCSS.HSF-IF.C.7A

What is the y-intercept of the function f(x) = -(x + 2)^2 - 3?

• (0, 7)

• (0, -3)

• (0, -7)

• (0, 3)

Tags

CCSS.HSF-IF.C.7A

Which point is the mirror image of the y-intercept in the graph of the function f(x) = -(x + 2)^2 - 3?

• (4, -7)

• (-4, -7)

• (4, 7)

• (-4, 7)

Tags

CCSS.HSF-IF.C.7A