Modeling with Systems — Unit test Answers

Organizers of the town fair make a total of $706 from selling 164 hot dogs and 74 hamburgers at one of their concession stands. At their other concession stand, they make $884 by selling 256 hot dogs and 61 hamburgers. If the prices are the same at both concession stands, what is the price of a hot dog?

The table below shows the data for a car stopping on a wet road. What is the approximate stopping distance for a car traveling 35 mph? Car Stopping Distancesv(mph)d(ft)1517.92031.850198.7

Which equation represents a graph with a vertex at (1, –6)?

Which graph represents the solution set for the quadratic inequality x2 + 2x + 1 > 0?

Gabriella is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by where x and y are measured in inches. Where should she place the bulb to ensure a perfect beam of light?

Tim throws a stick straight up in the air from the ground. The function h = –16t2 + 48t models the height, h, in feet, of the stick above the ground after t seconds. Which inequality can be used to find the interval of time in which the stick reaches a height of more than 8 feet?

For what values of m does the graph of y = mx2 – 5x – 2 have no x-intercepts?

Louis used a quadratic equation to model the height, y, of a falling object x seconds after it is dropped. Which ordered pair generated by this model should be discarded because the values are unreasonable?

During a baseball game, a player hits a ball while a bird is flying across the field. Let t be the time in seconds since the ball is hit and h be the height in feet. The height of the baseball over time is modeled by the equation h = –16t2 + 65t and the height of a bird over time is modeled by the equation h = 8t + 20. What do the intersection points of the equations represent?

Which equation is y = –6x2 + 3x + 2 rewritten in vertex form?

What are the values of x in the equation x2 – 6x + 9 = 25?

During a pumpkin launching contest, two pumpkins are launched at the same time. The path of pumpkin A is modeled by the equation y = –0.01x2 + 0.32x + 4. The path of pumpkin B is modeled by the equation y = –0.01x2 + 0.18x + 5. If x represents the distance the pumpkin traveled in feet and y represents height of the pumpkin in feet, what does the intersection point of the equations represent?

If the discriminant of a quadratic equation is 4, which statement describes the roots?

What is the sum of 12 – 5i and –3 + 4i?