Quadratic Functions and Their Properties

The video tutorial demonstrates how to use the Desmos graphing calculator to solve quadratic problems from previous star tests. It covers finding the range of a quadratic equation and identifying the correct graph representation by analyzing the graph's features such as maximum values and intercepts. The tutorial emphasizes using Desmos to confirm answers and eliminate incorrect options.

What tool is being used to solve the problems in the video?

• A Desmos graphing calculator

• A spreadsheet software

• A traditional calculator

• A scientific calculator

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

• y values are greater than or equal to 4

• y values are less than or equal to 4

• y values are greater than or equal to -4

• y values are less than or equal to -4

What is the vertex of the parabola y = -x^2 - 2x + 3?

• (2, -1)

• (1, -4)

• (-1, 4)

• (0, 3)

Which of the following is true about the graph of y = -x^2 - 2x + 3?

• It opens upwards and has a minimum

• It opens downwards and has a maximum

• It opens downwards and has a minimum

• It opens upwards and has a maximum

What is the equation of the second quadratic function discussed?

• y = -x^2 - 6x + 1

• y = -x^2 + 6x - 1

• y = x^2 + 6x - 1

• y = x^2 - 6x + 1

What is the maximum value of the function y = -x^2 + 6x - 1?

• 10

• 8

• 6

• 4

How many x-intercepts does the graph of y = -x^2 + 6x - 1 have?

• Three

• Two

• One

• None

Which graph feature helps in identifying the correct graph of y = -x^2 + 6x - 1?

• The number of x-intercepts

• The symmetry of the graph

• The slope of the graph

• The y-intercept

What is the significance of the maximum value in the graph of y = -x^2 + 6x - 1?

• It is irrelevant to the graph

• It determines the y-intercept

• It indicates the highest point on the graph

• It shows the lowest point on the graph

Which graph has a maximum value of 8?

• Graph A

• Graph D

• Graph B

• Graph C