UNIT 3 TEST - PART 2

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-intercept of the graph of the function.

Front

How do you find the zeros of a quadratic function?

Back

To find the zeros of a quadratic function, you can set the function equal to zero and solve for x using factoring, the quadratic formula, or completing the square.

Front

What does it mean if a function has no x-intercepts?

Back

If a function has no x-intercepts, it means that there are no real values of x for which the function equals zero.

Front

What is the significance of the x-intercept in a graph?

Back

The x-intercept is the point where the graph of the function crosses the x-axis, indicating the values of x that make the function equal to zero.

Front

If a function has zeros at x = -3 and x = 1, what does this indicate about its graph?

Back

This indicates that the graph of the function crosses the x-axis at the points (-3, 0) and (1, 0).

Front

What is the relationship between the zeros of a function and its factors?

Back

The zeros of a function correspond to the values of x that make each factor of the function equal to zero.

Front

How can you verify if a given value is a zero of a function?

Back

To verify if a value is a zero of a function, substitute the value into the function. If the result is zero, then it is a zero of the function.

Front

What is the quadratic formula used for?

Back

The quadratic formula is used to find the zeros of a quadratic function in the form ax^2 + bx + c = 0, given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the term 'multiplicity' refer to in relation to zeros?

Back

Multiplicity refers to the number of times a particular zero appears as a root of the function. A zero with an even multiplicity touches the x-axis, while one with an odd multiplicity crosses it.

Front

If a function has a zero at x = 2 with a multiplicity of 3, what does this imply?

Back

This implies that the graph of the function touches the x-axis at x = 2 and does not cross it, creating a 'bounce' effect.