Understanding Quadratic Functions and Their Properties

This video tutorial explains how to graph quadratic functions in standard form. It covers the transformation from general to standard form, identifying the vertex, and understanding the effects of the coefficient 'A' on the parabola's direction and shape. The tutorial includes examples demonstrating how to find the vertex, axis of symmetry, and intercepts, and how to sketch the graph of quadratic functions.

What is the standard form of a quadratic function?

• f(x) = ax^2 + bx + c

• f(x) = a(x - h)^2 + k

• f(x) = ax + b

• f(x) = a(x + h)^2 - k

If 'a' is negative in the standard form of a quadratic function, what is the direction of the parabola?

• It opens upwards

• It opens downwards

• It opens to the right

• It opens to the left

How does increasing the value of 'a' affect the graph of a quadratic function?

• The parabola shifts to the right

• The parabola shifts to the left

• The parabola becomes narrower

• The parabola becomes wider

What happens to the parabola when the value of 'h' is increased?

• It shifts to the left

• It shifts to the right

• It shifts downwards

• It shifts upwards

In the example, what is the vertex of the quadratic function y = (x - 3)^2 - 4?

• (-3, 4)

• (3, -4)

• (-3, -4)

• (3, 4)

What is the equation of the axis of symmetry for the function y = (x - 3)^2 - 4?

• y = 3

• x = -3

• x = 3

• y = -3

How do you find the y-intercept of a quadratic function in standard form?

• Set both x and y to zero

• Set y to zero and solve for x

• Set x to zero and solve for y

• Set the vertex to zero

In the second example, what is the y-intercept of the function y = -2(x + 1)^2 + 8?

• (0, -6)

• (0, -8)

• (0, 6)

• (0, 8)

What is the x-intercept of the function y = -2(x + 1)^2 + 8 when solved?

• (0, 1) and (0, -1)

• (1, 0) and (-3, 0)

• (3, 0) and (-1, 0)

• (2, 0) and (-2, 0)

What is the significance of the axis of symmetry in a parabola?

• It is the line that divides the parabola into two symmetrical halves

• It indicates the maximum point of the parabola

• It shows the direction in which the parabola opens

• It determines the width of the parabola