Finding Zeros of Quadratic Functions by Factoring

This lesson teaches how to find zeros of quadratic functions by factoring. It explains the Zero Product Property, demonstrates finding zeros in both factored and non-factored forms, addresses common misunderstandings, and compares zeros of different functions. The zeros correspond to the x-intercepts on a graph.

What does the Zero Product Property state?

• If a product is zero, one or more factors must be zero.

• If a product is zero, all factors must be zero.

• If a product is zero, none of the factors can be zero.

• If a product is zero, the product must be negative.

When a function is already in factored form, what is the first step to find its zeros?

• Add all factors together.

• Divide the function by its leading coefficient.

• Multiply all factors together.

• Set the function equal to zero.

What is a common misunderstanding when finding zeros in factored form?

• Thinking a constant factor can be zero.

• Thinking a variable factor cannot be zero.

• Thinking all factors must be zero.

• Thinking the product must be positive.

What must be done first when a function is not in factored form?

• Graph the function.

• Add a constant to the function.

• Factor the function.

• Set the function equal to zero.

How can you verify the zeros of a function graphically?

• By checking the maximum point of the graph.

• By checking the slope of the graph.

• By checking the y-intercepts.

• By checking the x-intercepts.

What is the result when two factors of a function are the same?

• There are no zeros.

• There is only one zero.

• There are two distinct zeros.

• The zeros are imaginary.

What is the significance of x-intercepts in the context of zeros?

• They indicate the points where the graph crosses the x-axis.

• They indicate the points where the graph crosses the y-axis.

• They indicate the slope of the graph.

• They indicate the maximum points of the graph.