Exploring the Characteristics of Quadratics

This video tutorial covers the key characteristics of quadratic equations, including how to find the y-intercept, zeros, turning point, axis of symmetry, domain, and range. It also explains how to identify increasing and decreasing intervals, as well as positive and negative intervals on a graph. The tutorial uses a specific quadratic equation, y = x^2 - 4x + 3, to illustrate these concepts through graphs and tables.

What is the y-intercept of the quadratic equation y = x^2 - 4x + 3?

• (0, -4)

• (0, 4)

• (0, -3)

• (0, 3)

How do you find the y-intercept from the standard form of a quadratic equation?

• Set x to 1

• Set y to 0

• Set x to 0

• Set y to 1

What are the zeros (roots) of the quadratic equation y = x^2 - 4x + 3?

• x = 1 and 3

• x = -1 and -3

• x = 2 and -2

• x = 0 and 4

What is another term for the zeros of a quadratic equation?

• Vertices

• Roots

• Intercepts

• Slopes

What is the turning point (vertex) of the quadratic equation y = x^2 - 4x + 3?

• (1, 1)

• (1, -1)

• (2, 1)

• (2, -1)

What is the axis of symmetry for the quadratic equation y = x^2 - 4x + 3?

• x = 1

• x = 3

• x = 2

• x = 4

What is the domain of the quadratic function y = x^2 - 4x + 3?

• x = 0

• x > 0

• All real numbers

• x < 0

What is the range of the quadratic function y = x^2 - 4x + 3?

• y ≥ -1

• y ≤ -1

• y < 0

• y > 0

In which interval is the quadratic function y = x^2 - 4x + 3 increasing?

• (1, ∞)

• (2, ∞)

• (-∞, 1)

• (-∞, 2)

Where is the quadratic function y = x^2 - 4x + 3 positive?

• x < 0 and x > 4

• x > 1 and x < 3

• x < 1 and x > 3

• x = 1 and x = 3