Reporting Category 3: Properties of Quadratic Functions
Algebra 2: RC 3
2A.6B (R)
Marco was observing the path of a hot air balloon as it rose slightly and then descended. He recorded the balloon’s height, y, in feet, every minute, x, for 5 minutes. His observations are recorded in the table below.
1.Graph the data points.
2.Find a quadratic equation to help Marco model this situation.
3.When would the balloon be 174 feet above the ground?
4.What was the height of the balloon when Marco began collecting his data?
5.If the balloon’s path is modeled by the equation in #2, how many minutes after Marco sees it, will it touch the ground?
6.How many minutes had the balloon been in the air before Marco began recording data?
Algebra 2: RC 3
2A.6C (S)
1.Which of the following quadratic functions does not have zeros of -15 and 6?
A.f(x)= x²+3x-30C.f(x)=- x²-6x+60
B.f(x)= -x²-9x+90D.f(x)= -x²-9x-90
2.Which polynomial function has a zero 4+i?
F.g(x)=x²+8x+17H.g(x)=x²-8x-17
G.g(x)=x²-8x+17J.g(x)=x²+8x-17
3.Find the polynomial function with zeros ±2.
A.h(x)=x²-8C.h(x)=x²+8
B.h(x)=x²-8x+8D.h(x)=x²+4x-8
4.If a quadratic equation is graphed and has x-intercepts at -8 and 6, what is the quadratic function that corresponds with this situation?
F.f(x)=(x+1)²+49H.f(x)=(x+1)²-49
G.f(x)=(x-1)²+49J.f(x)=(x-1)²-49
5.p(x) has roots and - . Find p(x).
A.p(x)=12x²+5x+2C.p(x)=12x²-5x+2
B.p(x)=12x²-5x-2D.p(x)=12x²+5x-2
Algebra 2: RC 3
2A.8A (R)
1.The base of a triangle is 3 inches less than twice its height. If the area of the triangle is 126 square inches, which of the following equations can be used to find h, the height of the triangle in inches?
A.2h²-3h+63=0C.2h²-3h+252=0
B.2h²-3h-63=0D.2h²-3h-252=0
2.The product of two consecutive even integers is 728. If the greater of the two integers is n+6, write a quadratic equation that can be used to find both integers.
F.n²+14n-680=0H.n²+10n-704=0
G.n²+13n-686=0J.n²+11n-698=0
3.Write a quadratic function to model the function graphed below.
A.y=2x²+4x+300C.y= -x²+300
B.y= -2x²+4x+300D.y=-(x-300)²+13
Algebra 2: RC 3
2A.8A (R)
4.The area of a parallelogram is 143 square centimeters. The height of the parallelogram is one more than twice a number. The base is two less than three times the same number. Which of the following equations can be used to find the number, x?
F.6x²+x-145=0H.-6x²-x-141=0
G.-6x²+x-141=0J.6x²-x-145=0
5.The height of an isosceles trapezoid is three more than a number, x. The shorter base is one less than three times the same number. The other base is four more than three times the number. If the area of the isosceles trapezoid is 148.5 square feet, write a quadratic equation that can be solved to find x.
6.The largest flag flown from a flagpole is a Brazilian national flag measuring 100 meters by 70 meters in Brasilia, the capital of Brazil. Suppose a company wants to make a flag and increases the length and width of the flag by x feet. The area of the flag cannot exceed 10,000 square meters. Write an inequality to determine by how much the length and width can be increased.
Algebra 2: RC 3
2A.8B (S)
For #1-3, find the number of distinct roots and the nature of the roots (real, imaginary, rational, and irrational) for each quadratic equation.
1.A car is traveling at 26 meters per second and accelerating at -13 m/s². After traveling 26 m, the driver brings the car to a complete stop. The equation 26=26t - t², where t is the time it takes to stop, can be used to represent this situation.
2.A person’s blood pressure depends on her age. For women, normal systolic blood pressure is given by the formula P=0.01A²+0.05A+107, where P is the normal blood pressure in millimeters of mercury and A is the age.
3.Bryan Starr is a 17-year old high school senior from Upper Arlington, Ohio who started his own lawn service when he was 12. His business has grown substantially and he has been able to put away money for college, buy a truck, and invest in new lawn equipment to keep up with the growing demand for his services. Suppose his weekly revenue R can be represented by the formula R= -p²+50p-125, where p is the average price he charges for each lawn.
For #4-7, use the quadratic functions or equations in #1-3 to answer the following questions.
4.How long did it take the person in Question #1 to stop the car?
5.Find the approximate age of a woman whose blood pressure is 121 mm Hg.
6.Explain how Bryan could earn $400 each week.
Algebra 2: RC 3
2A.8B (S)
7.Is there a price he could charge that would make his weekly revenue $600?
8.Choose the false statement regarding the value of the discriminant of a quadratic equation.
F.If it is a perfect square, two real rational roots exist.
G.If it is zero, infinitely many roots exist.
H.If it is negative, two complex roots exist.
J.If it is not a perfect square, two real rational roots exist.
Algebra 2: RC 3
2A.8C (S)
1.Use the table of values for f(b) to find the roots of f(b).
b / -1 / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8f(b) / 3 / 0 / -2 / -3 / -3 / -2 / 0 / 3 / 7 / 12
2.Use the table of values for f(x) to find the zeros of f(x).
x / -9 / -6 / -3 / 0 / 3 / 6f(x) / 36 / 0 / -18 / -18 / 0 / 36
3.Use the graph below to solve 2x²+2x-4=0.
4.Although no one has found a formula that generates prime numbers, 18th century Swiss mathematician Leonhard Euler discovered that f(x)=x²+x+17 produces prime numbers up to a certain point. Based on the graph of f(x), what are the roots of the function?
Algebra 2: RC 3
2A.8C (S)
5.In 1940, I.M. Chisov of the USSR bailed out of an airplane without a parachute at 21,980 feet and survived. The function h(t)= -16t²+21,980 describes the relationship between height h(t) in feet and the time t in seconds. Use the graph of the function to determine the number of seconds he fell before reaching the ground.
Algebra 2: RC 3
2A.8D (R)
1.The table below shows ordered pairs that satisfy the quadratic function f.
Based on the table, a solution to the equation f(x)=0 is found in which interval?
A.-2<x<-1C.1<x<2
B.-1<x<1D.3<x<5
2.The profit P, in dollars, for a company is modeled by the function P(x)= -75x²+15,000x, where x is the number of items produced. For which values of x will the company lose money?
F.x<2H.10≤x<20
G.2<x≤10J.x>20
Algebra 2: RC 3
2A.8D (R)
3.Which graph shows the solution set for the following inequality?
x²>x+12
4.The distance d that an object travels can be calculated when the initial speed , elapsed time t, and the rate of constant acceleration a are known. A formula that relates these factors is d(t)=t+at². If a motorcycle has an initial speed of 30 m/s and a constant acceleration of 6 m/s², how much time will it take to travel 200 m?
5.A ball is thrown straight up with an initial velocity of 56 ft/s. The height of the ball t seconds after it is thrown is given by the formula h(t)=56t-16t². After how many seconds will the ball return to the ground?
6.The Apollo 11 spacecraft propelled the first men to the moon and contained three stages of rockets. The first stage dropped off 2 minutes 40 seconds after takeoff and the second stage ignited. The initial velocity of the second stage was 2760 m/s with a constant acceleration of 200 m/s². How long did it take the second stage to travel 7040 m?
Algebra 2: RC 3
2A.8D (R)
7.The Empire State Building is 1250 feet tall. If an object is thrown upward from the top of the building at an initial velocity of 35 ft/s, its height t seconds after it is thrown is given by the function h(t)= -16t²+35t+1250. How long will it be before the object hits the ground?
Algebra 2STAAR Page 1