Understanding Quadratic Functions

The video tutorial explains how to express a quadratic function with given real solutions in factored form and then convert it to standard form. It discusses the impact of multiplying the function by constants on its zeros and identifies possible functions with the same zeros. The tutorial concludes by matching these functions with given choices.

What are the given solutions for the quadratic function f(x)?

• x = -3 and x = 5

• x = 3 and x = -5

• x = 0 and x = 5

• x = -3 and x = 0

How can a quadratic function be expressed using its solutions?

• As a sum of solutions

• As a product of linear factors

• As a single linear equation

• As a difference of squares

Why does the expression (x + 3)(x - 5) equal zero at the solutions?

• Because it is a constant function

• Because it is a linear equation

• Because it is a product of factors that equal zero

• Because it is a sum of squares

What is the first step in converting the expression (x + 3)(x - 5) to standard form?

• Divide the factors

• Multiply the factors

• Subtract the solutions

• Add the solutions

What is the standard form of the quadratic function derived from (x + 3)(x - 5)?

• x^2 - 8x + 15

• x^2 + 8x - 15

• x^2 - 2x - 15

• x^2 + 2x + 15

What happens to the zeros of the quadratic function if it is multiplied by a non-zero constant?

• The zeros become undefined

• The zeros become complex

• The zeros remain the same

• The zeros change

What is the result of multiplying the quadratic function by 2?

• 2x^2 + 8x + 30

• 2x^2 - 8x - 30

• 2x^2 + 4x + 30

• 2x^2 - 4x - 30

What is the result of multiplying the quadratic function by -2?

• -2x^2 + 8x + 30

• -2x^2 - 4x - 30

• -2x^2 - 8x - 30

• -2x^2 + 4x + 30

How do the graphs of the functions 2x^2 - 4x - 30 and -2x^2 + 4x + 30 compare?

• They are identical

• They have the same zeros but different shapes

• They have different zeros

• They are reflections of each other

Which of the following functions has the same zeros as the original quadratic function?

• -2x^2 + 4x + 30

• 3x^2 - 6x - 45

• 2x^2 - 4x - 30

• x^2 - 2x - 15