Graphing Quadratics with a Calculator

The video tutorial demonstrates how to use a TI-85 graphing calculator to graph quadratic equations and find their x-intercepts. It covers graphing y = -3x^2 + 4x - 1, finding its roots, and exploring a quadratic with no real roots. The tutorial also includes graphing a perfect square quadratic and identifying its vertex. The video emphasizes understanding the graphing process and interpreting results visually.

What is the primary purpose of using a graphing calculator in this video?

• To graph trigonometric functions

• To perform arithmetic operations

• To solve linear equations

• To find the roots of quadratic equations visually

Which calculator model is used in the video to graph the quadratic equation?

• TI-89

• TI-84

• TI-92

• TI-85

What is the first step in graphing the equation y = -3x^2 + 4x - 1 on the TI-85?

• Adjusting the window settings

• Pressing the ZOOM button

• Entering the equation in the y= menu

• Using the TRACE function

How is the x-intercept of the equation y = -3x^2 + 4x - 1 found using the calculator?

• By solving the equation algebraically

• By using the TRACE function to find where y equals zero

• By adjusting the window settings

• By using the CALC menu

What is the approximate value of the second x-intercept for y = -3x^2 + 4x - 1?

• 0.33

• 0.25

• 0.5

• 0.75

What conclusion is drawn about the quadratic equation y = 1/2x^2 - 2x + 3?

• It has one real x-intercept

• It has no real x-intercepts

• It has complex x-intercepts

• It has two real x-intercepts

What does the graph of y = 1/2x^2 - 2x + 3 indicate about its x-intercepts?

• The graph does not intersect the x-axis

• The graph intersects the x-axis at two points

• The graph intersects the x-axis at one point

• The graph is a straight line

What is the x-intercept of the equation x^2 + 6x + 9?

• 0

• 6

• -3

• 3

What is the significance of the vertex in the graph of x^2 + 6x + 9?

• It is the y-intercept

• It is the minimum point

• It is the only x-intercept

• It is the maximum point

What does a positive coefficient on x^2 indicate about the parabola's direction?

• It opens downward

• It opens upward

• It is a straight line

• It has no direction