Vertex and Axis of Symmetry

This video tutorial covers transformations of quadratic graphs, focusing on converting equations to vertex form. It begins with an introduction to the general form of a parabola and the concept of vertex form. The instructor explains the process of completing the square to rewrite equations in vertex form, providing detailed steps and examples. The tutorial includes solving example problems and graphing quadratic equations, highlighting key features such as the vertex and axis of symmetry. The video concludes with a demonstration of graphing techniques and reflections over the axis of symmetry.

What is the general form of a quadratic equation in vertex form?

• y = ax^2 + c

• y = ax^2 + bx + c

• y = a(x + h)^2 - k

• y = a(x - h)^2 + k

In the vertex form of a quadratic equation, what do the variables h and k represent?

• The vertex coordinates

• The x-intercept and y-intercept

• The axis of symmetry and vertex

• The slope and y-intercept

How do you determine the axis of symmetry from the vertex form of a quadratic equation?

• It is the y-coordinate of the vertex

• It is the x-coordinate of the vertex

• It is the sum of h and k

• It is the difference between h and k

What is the first step in completing the square for a quadratic equation?

• Divide the coefficient of x by 2 and square it

• Add the constant term to both sides

• Subtract the constant term from both sides

• Multiply the coefficient of x by 2

When completing the square, what do you do with the term (b/2)^2?

• Divide it by the coefficient of x

• Multiply it by the coefficient of x

• Subtract it from both sides of the equation

• Add it to both sides of the equation

In the example problem, what is the vertex of the equation y = (x + 5)^2 - 25?

• (5, -25)

• (5, 25)

• (-5, -25)

• (-5, 25)

What is the axis of symmetry for the equation y = (x + 5)^2 - 25?

• x = -5

• y = 25

• y = -25

• x = 5

How do you handle a quadratic equation with no B term when completing the square?

• Assume B is -1

• Assume B is 0

• Assume B is 2

• Assume B is 1

What is the vertex of the equation y = x^2 + 3?

• (0, 3)

• (3, 0)

• (0, -3)

• (-3, 0)

In the example problem, what is the vertex of the equation y = (x + 4)^2 - 1?

• (4, 1)

• (-4, 1)

• (4, -1)

• (-4, -1)