Graphing Quadratic Functions: A Comprehensive Guide

The video tutorial covers graphing quadratic functions, starting with the basic steps to find the axis of symmetry and vertex. It demonstrates graphing the parent function f(x) = x^2, explaining domain and range. The tutorial then provides examples with x^2 - 4 and -x^2 + 2x + 3, showing how to find vertices, x-intercepts, and analyze the graph's properties. The video concludes with a discussion on how the sign of the leading coefficient affects the parabola's direction.

What is the first step in graphing a quadratic function?

• Determine the domain

• Find the axis of symmetry

• Plot the y-intercept

• Find the vertex

Which formula is used to find the axis of symmetry?

• x = -b/2a

• x = a/b

• x = -b/a

• x = b/2a

What is the vertex of the quadratic parent function f(x) = x^2?

• (0, 0)

• (1, 1)

• (2, 4)

• (-1, 1)

What is the range of the quadratic parent function f(x) = x^2?

• y > 0

• y ≥ 0

• y ≤ 0

• y < 0

For the function f(x) = x^2 - 4, what is the y-value of the vertex?

• -4

• 4

• -2

• 0

What are the x-intercepts of the function f(x) = x^2 - 4?

• (-4, 0) and (4, 0)

• (0, -4) and (0, 4)

• (-2, 0) and (2, 0)

• (-1, 0) and (1, 0)

What is the axis of symmetry for the function f(x) = -x^2 + 2x + 3?

• x = -1

• x = 0

• x = 1

• x = 2

What is the maximum y-value for the function f(x) = -x^2 + 2x + 3?

• 1

• 3

• 2

• 4

What is the domain of any quadratic function?

• All integers

• All negative numbers

• All positive numbers

• All real numbers

What determines the range of a quadratic function?

• The axis of symmetry

• The vertex

• The y-intercepts

• The x-intercepts