Finding Zeros Graphically

Front

What is a zero of a function?

Back

A zero of a function is a value of x for which the function f(x) = 0. It represents the x-intercepts of the graph.

Front

How can you find zeros graphically?

Back

You can find zeros graphically by identifying the points where the graph of the function intersects the x-axis.

Front

What does it mean if a function has multiple zeros?

Back

If a function has multiple zeros, it means there are several x-values where the function equals zero, indicating multiple x-intercepts on the graph.

Front

What is the significance of the x-axis in finding zeros?

Back

The x-axis represents the output value of zero. Finding where the graph crosses the x-axis helps identify the zeros of the function.

Front

If a function is represented as f(x) = (x+1)(x-3), what are the zeros?

Back

The zeros are x = -1 and x = 3, found by setting each factor equal to zero.

Front

What is the relationship between zeros and factors of a polynomial?

Back

The zeros of a polynomial are the values of x that make the polynomial equal to zero, and they correspond to the factors of the polynomial.

Front

How do you determine the number of zeros a polynomial can have?

Back

A polynomial of degree n can have at most n zeros, considering multiplicity.

Front

What is the multiplicity of a zero?

Back

The multiplicity of a zero refers to the number of times a particular zero appears as a root of the polynomial.

Front

What does it indicate if a zero has an even multiplicity?

Back

If a zero has an even multiplicity, the graph touches the x-axis at that zero but does not cross it.

Front

What does it indicate if a zero has an odd multiplicity?

Back

If a zero has an odd multiplicity, the graph crosses the x-axis at that zero.