Finals Review

Front

Determine the x-intercepts of the function f(x)=(x+3)(x−1)(x−2)

Back

The x-intercepts are the values of x that make f(x) = 0. For f(x)=(x+3)(x−1)(x−2), the x-intercepts are -3, 1, and 2.

Front

What are the roots of the function f(x)=3x(x−4)(x+5)?

Back

The roots of the function are the values of x that make f(x) = 0. For f(x)=3x(x−4)(x+5), the roots are -5, 0, and 4.

Front

Solve the rational equation: (x+2)/(x-1) = 3

Back

To solve for x, cross-multiply: x + 2 = 3(x - 1). This simplifies to x + 2 = 3x - 3, leading to x = 2.5.

Front

What is the solution set for the graph of f(x) = (x-2)(x+2)?

Back

The solution set is the x-values where f(x) = 0. For f(x) = (x-2)(x+2), the solution set is {2, -2}.

Front

Solve the rational equation: (2x)/(x-3) = 4

Back

Cross-multiply to get 2x = 4(x - 3). This simplifies to 2x = 4x - 12, leading to x = 6.

Front

What is the definition of a root of a polynomial function?

Back

A root of a polynomial function is a value of x for which the function equals zero.

Front

Explain the concept of x-intercepts in a graph.

Back

X-intercepts are points where the graph of a function crosses the x-axis, meaning the output (y-value) is zero.

Front

What is the difference between a root and an x-intercept?

Back

A root refers to the solution of the equation f(x) = 0, while an x-intercept is the point on the graph where the function crosses the x-axis.

Front

How do you find the x-intercepts of a quadratic function?

Back

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

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation ax² + bx + c = 0.