Algebra 2 Final Exam

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For example, if a graph shows a drone's height above the ground, the domain might be the range of distances the drone can fly.

To find the vertex form of a quadratic function after transformations, apply the transformations to the parent function $$y=x^2$$ . For example, reflecting across the x-axis and shifting down and right results in the equation $$y=-\left(x-4\right)^2-5$$ .

The formula for calculating simple interest is $$P=rt$$ , where P is the interest, r is the rate, and t is the time.

The maximum or minimum value of a quadratic function in the form $$f(x)=ax^2+bx+c$$ can be found using the vertex formula $$x=-\frac{b}{2a}$$ . Substitute this x-value back into the function to find the corresponding y-value.

Simplifying an algebraic expression means to combine like terms and reduce the expression to its simplest form. For example, $$\left(18-2x^3+9x\right)-\left(4-x^2-3x^3+11x\right)$$ simplifies to $$x^3+x^2-2x+14$$ .

The x-axis typically represents the independent variable, while the y-axis represents the dependent variable. In the context of a drone's flight, the x-axis could represent distance traveled, and the y-axis represents height above ground.

A quadratic function is a polynomial function of degree 2, typically written in the form $$f(x)=ax^2+bx+c$$ , where a, b, and c are constants and $$a \neq 0$$ .

Reflecting a graph across the x-axis means that for every point (x, y) on the graph, there is a corresponding point (x, -y). This transformation changes the sign of the y-coordinates.

The vertex of a quadratic function in standard form $$f(x)=ax^2+bx+c$$ can be found using the formula $$x=-\frac{b}{2a}$$ . The y-coordinate can be found by substituting this x-value back into the function.

Standard form in algebra refers to writing an expression or equation in a conventional way. For polynomials, it means arranging terms in descending order of their degree.