Quadratic Functions and Graphing

This video tutorial explains how to find key characteristics of a quadratic function from its equation and graph it. It covers identifying coefficients, determining parabola orientation, calculating the vertex, finding vertical and horizontal intercepts, and establishing the axis of symmetry. The tutorial also includes graphing the parabola and understanding its domain and range.

What are the coefficients a, b, and c in the quadratic equation y = x^2 - 6x?

• a = 1, b = 0, c = -6

• a = 0, b = -6, c = 1

• a = 1, b = 6, c = 0

• a = 1, b = -6, c = 0

If a quadratic function has a positive 'a' value, in which direction does the parabola open?

• Downward

• Upward

• To the left

• To the right

How do you find the x-coordinate of the vertex for the quadratic equation y = ax^2 + bx + c?

• a divided by 2b

• Negative a divided by 2b

• Negative b divided by 2a

• b divided by 2a

What is the y-intercept of the quadratic function y = x^2 - 6x?

• (0, 6)

• (0, -6)

• (6, 0)

• (0, 0)

How do you determine the x-intercepts of a quadratic function?

• Solve for x when y is one

• Set y to zero and solve for x

• Set x to zero and solve for y

• Set both x and y to zero

What is the equation of the axis of symmetry for the quadratic function y = x^2 - 6x?

• x = 6

• x = -3

• x = 0

• x = 3

Which point is the vertex of the quadratic function y = x^2 - 6x?

• (6, 0)

• (0, 0)

• (3, -9)

• (3, 0)

What is the domain of any quadratic function?

• All real numbers

• All integers

• All negative numbers

• All positive numbers

What is the range of the quadratic function y = x^2 - 6x?

• y ≥ -9

• y ≤ -9

• y < -9

• y > -9

Using interval notation, how is the range of the function y = x^2 - 6x expressed?

• (-∞, -9]

• [-9, ∞)

• (-9, ∞)

• (-∞, 9]