Understanding Zeros of Functions

The video tutorial explains the concept of zeros of a function, which are the input values that make the function's output zero. It covers how to find zeros in both linear and quadratic functions using examples. The tutorial also discusses the graphical representation of zeros as x-intercepts and distinguishes between real and non-real zeros, emphasizing that real zeros correspond to x-intercepts on a graph.

What is a zero of a function?

• An input value that makes the function's output zero

• An output value that makes the function's input zero

• A point where the function has a maximum

• A point where the function has a minimum

In the equation y = 2x - 8, what value of x makes y zero?

• x = 8

• x = 2

• x = 4

• x = -4

What is the zero product property used for?

• To find the zeros of a quadratic function

• To calculate the y-intercept

• To find the maximum of a function

• To determine the slope of a line

If a quadratic equation is factored as (x + 2)(x - 2) = 0, what are the zeros?

• x = -2 and x = 0

• x = -2 and x = 2

• x = 2 and x = 4

• x = 0 and x = 2

For the function g, if it factors to (x + 4)(x - 3) = 0, what are the zeros?

• x = -4 and x = -3

• x = 4 and x = -3

• x = -4 and x = 3

• x = 4 and x = 3

What is the first step when factoring a quadratic with a negative leading coefficient?

• Multiply by a positive number

• Add a constant to both sides

• Factor out the negative

• Divide by the leading coefficient

What are the zeros of the function h if it factors to (2x + 3)(x - 1) = 0?

• x = 3 and x = -1

• x = -3/2 and x = 1

• x = 3/2 and x = -1

• x = -3 and x = 1

What do x-intercepts of a graph represent in terms of zeros?

• The minimum points of the function

• The maximum points of the function

• The imaginary zeros of the function

• The real zeros of the function

If a graph does not cross the x-axis, what can be said about its real zeros?

• It has no real zeros

• It has infinite real zeros

• It has two real zeros

• It has one real zero

What is the significance of a function touching the x-axis at a point?

• It indicates a point of inflection

• It indicates a zero of the function

• It indicates a minimum point

• It indicates a maximum point