Quadratic Functions and Their Properties

The video tutorial covers solving various quadratic problems, including graph equations, finding x-intercepts, using the quadratic formula, determining the range, identifying the axis of symmetry, converting to vertex form, finding maximum values, solving complex solutions, fitting equations to points, and maximizing revenue using a quadratic model.

Which feature helps in identifying the correct equation for a graph that opens downward?

• Positive x squared term

• Negative x squared term

• Positive y-intercept

• Negative y-intercept

What is the first step in finding the x-intercepts of the equation y = 2x^2 + 10x - 28?

• Replace x with zero

• Use the quadratic formula

• Replace y with zero

• Divide by the greatest common factor

Which method is used to solve the equation 35x^2 - 3x - 54 = 0?

• Factoring

• Graphing

• Completing the square

• Quadratic formula

What is the range of the function y = 4 + (x + 3)^2?

• y ≥ -3

• y ≤ 4

• y ≤ -3

• y ≥ 4

How do you find the axis of symmetry for the equation y = -x^2 + 4x + 5?

• x = -b/2a

• x = b/2a

• x = -a/2b

• x = a/2b

What is the vertex form of the equation y = x^2 + 6x + 7?

• y = (x - 3)^2 - 2

• y = (x + 3)^2 + 2

• y = (x + 3)^2 - 2

• y = (x - 3)^2 + 2

What is the maximum value of the function y = 3 - (x + 5)^2?

• -3

• 5

• -5

• 3

Which equation contains the solutions 3 + 5i and 3 - 5i?

• x^2 + 6x + 34 = 0

• x^2 + 6x - 34 = 0

• x^2 - 6x - 34 = 0

• x^2 - 6x + 34 = 0

How many books should be sold to maximize the revenue modeled by r(x) = 1500 + 80x - 0.01x^2?

• 2000

• 3000

• 4000

• 5000

What is the maximum revenue for the function r(x) = 1500 + 80x - 0.01x^2?

• 161,500

• 150,000

• 160,000

• 162,000