How to determine the domain and range of a quadratic using its vertex

The video tutorial explains how to determine if a quadratic function has a maximum or minimum value based on the coefficient 'a'. It covers finding the vertex of the parabola using the formula -b/2a and calculating the maximum value by substituting the x-value into the function. The tutorial also discusses the domain and range of the function, emphasizing that the domain is all real numbers while the range is limited by the maximum value.

What determines if a quadratic function has a maximum or minimum value?

• The value of 'b'

• The value of 'c'

• The sign of 'a'

• The value of 'x'

What is the formula to find the x-coordinate of the vertex of a quadratic function?

• b/2a

• a/2b

• -b/2a

• -a/2b

If the x-coordinate of the vertex is 1, what is the next step to find the maximum value of the function?

• Find the derivative

• Use the quadratic formula

• Substitute x = 1 into the function

• Calculate the integral

What is the maximum value of the function f(x) = -2x^2 + 4x - 3?

• 0

• -1

• 2

• 1

What is the domain of a quadratic function?

• Only positive numbers

• All real numbers

• Numbers between -1 and 1

• Only negative numbers

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

• [0, ∞)

• (-∞, ∞)

• (-∞, -1]

• [-1, ∞)

If a quadratic function opens upwards, what can be said about its range?

• It is constant

• It is undefined

• It has a maximum value

• It has a minimum value