CW - Oct 9-10 - Zeros, Roots, and Intercepts

What is the difference between a zero and a root of a function?

• A zero of a function is a specific type of root where the function equals zero.

• A root of a function is a point where the function is undefined.

• A zero of a function is a point where the function is undefined.

• A root of a function is a specific type of zero where the function equals one.

Find the zeros of the function f(x) = 2x^2 - 5x + 3.

• x = 4

• x = 3/2, x = 1

• x = 2

• x = -1/2

Determine the roots of the equation 3x^2 + 4x - 2 = 0.

• x = (-2 ± √10) / 3

• x = (-2 ± √10) / 5

• x = (-2 ± √10) / 4

• x = (-2 ± √10) / 2

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

• The x-intercepts are the same as the zeros of the function, and the y-intercept is the value of the function when x equals zero.

• The intercepts of a function are always equal to its zeros.

• The x-intercepts are the values of the function when y equals zero, and the y-intercept is the value of the function when x equals zero.

• The intercepts of a function are always positive values.

Solve the equation 4x - 8 = 0 to find the x-intercept.

• 4

• 0

• 2

• -2

Find the y-intercept of the function g(x) = -3x + 2.

• -3

• 0

• 1

• 2

How can you determine the number of zeros a polynomial function has?

• By finding the constant term of the polynomial and counting the number of distinct real roots.

• By finding the degree of the polynomial and counting the number of distinct real roots.

• By finding the sum of the coefficients of the polynomial and counting the number of distinct real roots.

• By finding the leading coefficient of the polynomial and counting the number of distinct real roots.

Solve the equation x^3 - 8 = 0 to find the zeros.

• x = 0

• x = 4

• x = -2

• x = 2

What is the significance of the x-intercept in a real-world context?

• The x-intercept represents the value of the independent variable at which the dependent variable is at its peak.

• The x-intercept represents the value of the independent variable at which the dependent variable becomes zero.

• The x-intercept represents the average value of the dependent variable.

• The x-intercept represents the maximum value of the dependent variable.

Find the roots of the quadratic equation 2x^2 + 5x + 3 = 0.

• The roots of the quadratic equation 2x^2 + 5x + 3 = 0 are -1 and -3/2.

• The roots of the quadratic equation 2x^2 + 5x + 3 = 0 are 1 and -3/2.

• The roots of the quadratic equation 2x^2 + 5x + 3 = 0 are -1 and 3/2.

• The roots of the quadratic equation 2x^2 + 5x + 3 = 0 are 1 and 3/2.