Math 3 wk 3

Front

What is the y-intercept of a cubic function?

Back

The y-intercept is the point where the graph intersects the y-axis. For the function f(x) = ax^3 + bx^2 + cx + d, the y-intercept is found by evaluating f(0) = d.

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation ax^2 + bx + c = 0 by factoring, express it in the form (x - p)(x - q) = 0, where p and q are the roots. Set each factor to zero to find the solutions.

Front

What are the factors of the polynomial x^3 + 7x^2 + 7x - 15 when divided by (x - 1)?

Back

The factors are (x - 1)(x + 5)(x + 3).

Front

How do you find the zeros of a function?

Back

To find the zeros of a function, set the function equal to zero and solve for x. The solutions are the x-values where the graph intersects the x-axis.

Front

What is the result of multiplying (x - 4)(x - 6)?

Back

The result is x^2 - 10x + 24.

Front

What is a cubic function?

Back

A cubic function is a polynomial function of degree three, typically in the form f(x) = ax^3 + bx^2 + cx + d.

Front

What does it mean for a polynomial to be factored?

Back

Factoring a polynomial means expressing it as a product of its factors, which can be simpler polynomials or numbers.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

How do you determine the vertex of a quadratic function?

Back

The vertex of a quadratic function in standard form y = ax^2 + bx + c can be found using the formula x = -b/(2a) and then substituting x back into the equation to find y.

Front

What is the difference between a polynomial and a monomial?

Back

A polynomial is a sum of multiple terms (e.g., ax^2 + bx + c), while a monomial is a single term (e.g., ax^n).