Modeling with Systems — Cumulative exam Answers

What is the completely factored form of 8x2 – 50?

Which value must be added to the expression x2 – 3x to make it a perfect-square trinomial?

Subtract from .

One root of is x = –10. What are all the roots of the function? Use the Remainder Theorem.

Which expression is equivalent to ? Assume x 0 and .

Matteo is adjusting a satellite because he finds it is not focusing the incoming radio waves perfectly. The shape of his satellite can be modeled by where x and y are modeled in inches. He realizes that the static is a result of the feed antenna shifting slightly off the focus point. What is the focus point of the satellite?

Jalen solved the equation by graphing. Which graph can Jalen use to show his solution?

Which graph includes a function, its inverse, and a dashed line that verifies the relationship?

Which is the standard form of the equation of a parabola with a focus of (8, 0) and directrix x = –8?

Use synthetic division to solve . What is the quotient?

The financial planner for a beauty products manufacturer develops the system of equations below to determine how many combs must be sold to generate a profit. The linear equation models the income, in dollars, from selling x plastic combs; the quadratic equation models the cost, in dollars, to produce x plastic combs. According to the model, for what price is each comb being sold?

What are the domain and range of f(x) = |x + 6|?

The matrix below represents a system of equations.Which matrix represents the solution to this system of equations?

Given the function f(x) = 3|x – 2| + 6, for what values of x is f(x) = 18?

Which graph shows the solution to the system of inequalities below?

The quotient of (x4 – 3x2 + 4x – 3) and (x2 + x – 3) is a polynomial. What is the quotient?

Hiroto solved the equation 6 – 4|2x – 8| = –10 for one solution. His work is shown below.6 – 4|2x – 8| = –10 –4|2x – 8| = –16|2x – 8| = 42x – 8 = 42x = 12 x = 6

As Tia solved the system of equations below, she transformed matrices at different steps during the process.She noted the following matrices.IIIIIIIVIn which order should the matrices be arranged when solving the system from start to finish?

Based on the type of equations in the system, what is the greatest possible number of solutions?

Which two functions are inverses of each other?