Quadratic equations Questions and Answers

13 Calculate the ag term of the geometric sequence with a3 16 and r O 16384 O O 16 O 65536 64 None of these are correct

P x x3 3x2 11x 33 Step 1 of 2 Use the Rational Zero Theorem to list all of the potential rational zeros Answer Enter only the positive values Separate multiple answers with commas

Consider the following polynomial g x x4 7x 11x 7x 12 Step 2 of 2 Use polynomial division and the quadratic formula if necessary to identify the actual zeros Answer Separate multiple answers with commas

Labor Information Regular Rate 16 00 hr Overtime Rate 23 50 hr Targeted Labor Cost 12 000 wk Labor Hours Needed 750 wk Any hour worked over 40 hrs wk must be paid overtime rate a 14 person team how does the actual weekly labor cost compare to the target 16 over target 300 over target 1 160 over target 1 425 over target 5 625 over target

gas price occurred most often 3 59 7 Cole bought 10 gallons of gas at the gas station with the lowest price He paid with two 20 bills Write and solve an equation to find his change 520 13 57 DATA 3 61 3 59 3 58 Prices of One Gallon of Gas c Thursday in dollars 3 60 3 59 3 58 3 60 3 61 3 62 3 57 3 59 3 60

D 1 2x 5x 5x is a linear combination of the set S containing the vectors 5 5x x x 5 4 5x 5x x 5 4x 2x 2x The corresponding linear combination would be 1 2x 5x 5x 15 5x x x 4 52 5x2 x 5 4x 2x 2x

b The base is a square Determine the surface area in square feet and volume in cubic feet of the following Round your answers to one decimal place 55 ft surface area volume 120 ft z ft2 ft3 3

d Find the area of the shaded portion in the given diagram A m 284 6 m 110 3m 195 6m

multiple answer options for part b concave up concave down Consider the function f x x 20 f x has two inflection points at x C and x D with C D where C is and D is Finally for each of the following intervals tell whether f x is concave up or concave down o C Select an answer C D Select an answer D o Select an answer 4

Algebra the function is concave down on La gr fica de la funci n r se lustra a continuaci n Esta funci n es c ncava hacia abajo en Seleccione una O a 00 0 5 U 0 5 00 O b 0 5 0 5 05 0 5 Q

Solve the nonlinear system algebraically Graph the equations and explici display the solutions to the system x 49 y x 6x 7

Solve the triangle Round your answers to one decimal place a 71 2 m c 44 7 m B 13 5 b A 11 m

domain vertical asymptote x intercept Sketch its graph by hand 10 x 1 x y y 10 101 10 X 5 x 10 x 10 10 5 10 10

A chemical company makes two brands of antifreeze The first brand is 30 pure antifreeze and the second brand is 45 pure antifreeze In order 90 gallons of a mixture that contains 40 pure antifreeze how many gallons of each brand of antifreeze must be used

Handball Football Handball 20 Basketball 5 TOTAL STUDENTS 1 How many students do not like either Handball or Football 21 2 How many students like Handball or Basketball 3 How many students like both Football and Basketball but not Handball 4 How many students do not like both Handball and Basketball 5 How many students do not like both Football and Basketball 6 How many students like both Handball and Basketball but not Football 7 How many students like both Handball and Football but not Basketball B How many students like both Handball and Football 9 How many students like Handball or Football or Basketball 10 How many students like both Handball and Basketbal

Use the table to answer the following questions C 0 1 2 5 6 7 f x 27 15 51 4 3 9 Evaluate f 3 3 88 00 4 61 f 3 8 80 9 82

f K can result directly from the fact that AB CD AB CD ng statements BCA 4DAC ABC ADC BAC 4DCA

2 Find the equation of the polynomial with roots 3 0 and 4i 0 real coefficients and passing through the point 1 34 O A f x 3x4 39x 144 O B f x x4 13x2 48 O C f x 3x4 39x 144 O D f x x4 13x2 48

A child has a bottle full of pennies nickels dimes and quarters There are twice as many quarters as pennies four times as many nickels as pennies and five times as many dimes as nickels How many more dimes does the child have than quarters O 4 times as many 10 times as many 20 times as many 5 times as many O 0

3 A rocket is launched from a platform 14 feet above the ground and follows a parabolic path represented by the equation R x x 8x 14 where x represent time in seconds At the same time a flare is fired from 6 feet above the ground and follows a straight path represented by the equation F x x 6 Graph and label both equations on the accompanying grid Will the rocket and flare ever collide Justify your answer

Quadratic Linear Systems Solve each system of equations graphically and check 1 f x x 4x 1 g x 2x 1

3 b f x 2x Vertical Intercept Horizontal Intercept s Vertex c g x 5x 4 Vertical Intercept Horizontal Intercept s Vertex d h x 4x 2x Vertical Intercept Horizontal Intercept s Vertex

6 Complete the table Show your work You can write the vertex you found from Problem 2 a f x 21 21 3 b g x 3x 2 c Function d f x 1 3 h z 3r Vertex Vertical Intercept Vertex 7 For each quadratic function below Graph the function on your calculator using an appropriate viewing window Draw the graph neatly below Label the vertical intercept Horizontal Intercept s Domain Determine the vertex Mark and label the vertex on the graph Determine the horizontal intercepts if they exist and label them on the graph a f x 2r 6x 3 Range

c h x 2x2 6x 4 a Vertical Intercept Which direction does this parabola open Why d f x x 3x a Vertical Intercept Which direction does this parabola open Why e g x a 2 3 b Vertical Intercept Which direction does this parabola open Why

Question 3 Evaluate the expression k 7 p 3 yz for k 5 p 4 y 6 z 1 Show your work leading to the answer

Question 2 Evaluate the expression Write down all the steps leading to the answer to receive full credit Don t use a calculator 30 5 3 15 2 3

graph Which graph represents the function of f x the quantity of 9 x squared minus 36 all over 3 x plus 6

Ex 6 Write an equation in intercept form for the graph of a degree 4 quartic polynomial with single roots 3 and 6 and a double root at 1 Also include the fact that it falls on the left Sketch the graph

for the graph of a degree 4 quartic polynomial with single roots 3 and 6 and a double root at 1 Also include the fact that it falls on the left Sketch the graph

tan 2 pi x tanx Note that each Statement must be based on a Rule chosen from the

For what values of m does the graph of y mx 2 5x 2 have no x intercept s

Plot the point that is symmetric to 3 8 with respect to the x axis

In you quadratic equation Core Concepts Solving Quadratic Equations by Graphing Step 1 Write the equation in standard form ax bx c 0 Step 2 Graph the related function y ax bx c Step 3 Find the x intercepts if any 2 Ihr c 0 are the x intercepts of the graph

Number of Solutions of a Quadratic Equation A quadratic equation has two real solutions when the graph of its related function has two x intercepts one real solution when the graph of its related function has one x intercept no real solutions when the graph of its related function has no x intercepts Notes

Solve each equation round to the nearest thousandth if necessary a log7 6x17 3 b 2 log3 x log3 5

A night triangle has side lengths 3 4 and 5 as shown below Use these lengths to find cos M sin M and tan M COLM 100 0 M CO

station 4 b a Find the value of x Express c in terms of a and b 40 110

Given vector u 1 1 and v 4 2 find a linear combination of the vectors u and v of the form au bv that would result in the vector 12 0

Version A Solve the three equations below using the given solving method State whether the types of solution s are irrational or non real complex Answers should be left in exact radical form simplified and approximate decimal form rounded to nearest tenth 1 Solve by using zero product property 5x 12x 4 0 2 Solve by completing the square x 14x190 3 Solve by using quadratic formula 5x 7x 12 0

6 Set up trig equations to solve for x and y below Round your answers to the nearest tenth 21 90 X y 32 x y b A 20 foot ladder rests against a wall The base of the ladder is 7 feet from the wall What angle does the ladder make with the ground Round to the nearest whole number

Rewrite the following quadratic equation to graphing form Then find the key features and sketch unction f x x 2x 3 X Feature Vertex x intercept s y intercept Line of symmetry Domain Range Interval of increase Interval of decrease Description

10 8 6 4 2 6 5 4 3 2 1 IN 2 4 6 8 10 12 The function graphed above is 4 5 6 Concave up on the interval s Write your answer using interval notation Concave down on the interval s Write your answer using interval notation There is an inflection point at 1 2 p

Find the partial fraction decomposition for the following rational expression Answer A and B 3x 23 x 3 x 4 A x 3 B x 4

Evaluate each expression using the unit circle No decimal answers Show all work a sin 150 cos 300 sin 810 cos 240 b cos 210 cot 120 3 sin 135 c cos 150 cos 180 tan 240 D d tan 2 cos 2 csc

Simplify 1 Assume all variables are positive

Graph the funtion over a one period interval y cot x TOP 400AL 2

SORTABLE Question 6 Order the numbers below from smallest to largest 10 8 3 2 START ORDER

write an algebraic expression 1 a number plus 7 X minus 14 3 le times name the variable Cletter in each 4 16 3x 5 12c 4 Solve 6 m 15 7 4m 8 f 7 17 9 4n Combine when m 5 when m 2i when n 30 when n 6 like terms 10 2x 7y 8 11 3x 4x2 12 7y 3y 8x for

19 y tan x Amplitude Period Increment Asymptote

6 Use Gauss seidel method up to three iterations to solve the system of linear equations represented by A 2 6 3 1 8 1 7 X 2 Solve the percent relative errors 21 X2 X3 and B 38 34 20