Exploring Key Features of Quadratic Functions

The video tutorial reviews key features of quadratic functions, focusing on the three forms: standard, vertex, and factored. It explains how to identify graph features like the axis of symmetry, vertex, and intercepts. The tutorial demonstrates writing equations in vertex and factored forms, solving for 'a', and converting these forms to standard form. It also covers transformations from the quadratic parent function.

What is the standard form of a quadratic equation?

• y = a(x - m)(x - n)

• y = a(x - h)^2 + k

• y = ax^2 - bx - c

• y = ax^2 + bx + c

What does the vertex form of a quadratic equation highlight?

• The y-intercept of the graph

• The solutions or roots of the equation

• The maximum or minimum point of the graph

• The standard form conversion

What is the axis of symmetry in the given graph?

• x = 0

• x = -1

• x = 1

• x = 8

What is the minimum value of the quadratic function?

• 0

• -8

• 8

• -1

How do you determine the transformations from the parent function?

• By the vertex movement

• By the coefficient 'a'

• By the x-intercepts

• By the y-intercept

What is the value of 'a' when converting to vertex form?

• 1

• -1

• 2

• 3

What are the roots of the quadratic function from the graph?

• -1 and 8

• 2 and -2

• -3 and 1

• 0 and -6

In the factored form, what does 'a' represent?

• The vertex of the parabola

• The direction and width of the parabola

• The x-intercepts of the graph

• The y-intercept of the graph

How do you convert from vertex form to standard form?

• By factoring

• By completing the square

• By finding the roots

• By expanding and simplifying

What is the result of converting the factored form to standard form?

• y = 2x^2 + 4x - 6

• y = x^2 + 4x + 6

• y = 2x^2 - 4x + 6

• y = x^2 - 4x - 6