Finding Zeros of a Quadratic Function by Factoring a Trinomial

This video tutorial explains how to find the zeros of a quadratic function by factoring a trinomial. It covers the zero product property, the difference between standard and factored forms, and common misunderstandings in factoring. The tutorial demonstrates finding zeros for the function 2x squared plus 3x minus 2 and verifies the solutions by substitution.

What does the zero product property state?

• If the product of two factors is zero, neither factor can be zero.

• If the product of two factors is zero, the factors are equal.

• If the product of two factors is zero, at least one factor must be zero.

• If the product of two factors is zero, both factors must be zero.

Which of the following is the correct standard form of a quadratic polynomial?

• ax^2 + bx + c

• ax + bx^2 + c

• bx + ax^2 + c

• ax^2 + c + bx

What is a common misunderstanding about factored form?

• Factored form must have all factors as prime.

• Factored form is the same as standard form.

• Factored form is only for linear polynomials.

• Factored form always contains parentheses.

In the example provided, what are the zeros of the function f(x) = 2x^2 + 3x - 2?

• 0 and 2

• 1/2 and -2

• 1 and -2

• 2 and -1/2

How can you verify the zeros of a quadratic function?

• By ensuring the function is in standard form.

• By graphing the function and finding the vertex.

• By checking if the function equals zero at those points.

• By multiplying the zeros together.