Understanding Quadratic Functions

This video tutorial covers the key components of quadratic functions, including how to determine the direction of a parabola, find the vertex, and identify intercepts. It also explains how to graph the function, determine the axis of symmetry, and understand the domain and range. The example used is y = -x^2 - 6x - 5, and the video provides step-by-step instructions for each calculation.

What is the value of 'a' in the quadratic equation y = -x² - 6x - 5?

• -5

• 6

• -1

• 1

If the coefficient 'a' is negative, in which direction does the parabola open?

• Downwards

• To the right

• Upwards

• To the left

How do you calculate the x-coordinate of the vertex of a quadratic function?

• -c/a

• b/2a

• -b/2a

• c/a

What is the y-intercept of the quadratic function y = -x² - 6x - 5?

• (0, 5)

• (-5, 0)

• (0, -5)

• (5, 0)

Which method can be used to find the x-intercepts of a quadratic equation?

• Completing the square

• All of the above

• Factoring

• Using the quadratic formula

What is the equation of the axis of symmetry for the given quadratic function?

• x = -3

• y = 3

• y = -3

• x = 3

Which point is the vertex of the parabola y = -x² - 6x - 5?

• (4, -3)

• (-4, 3)

• (3, -4)

• (-3, 4)

What is the domain of any quadratic function?

• Integers only

• Positive numbers only

• Negative numbers only

• All real numbers

What is the range of the quadratic function y = -x² - 6x - 5?

• y ≤ 4

• y ≥ 4

• y ≤ -4

• y ≥ -4

In interval notation, how is the range of the function y = -x² - 6x - 5 expressed?

• (-∞, -4]

• [4, ∞)

• [-4, ∞)

• (-∞, 4]