Quadratic equations Questions and Answers

Express as a product In 5 In 5 Simplify your answer Use integers or fractions for any numbers in the ex

Find a polynomial with real coefficients that has the given zeros 1 and 4 3i 3 One such polynomial P x can be defined as P x x 7x x 25

2 Solve the system or show that it has no solution If there is no solution enter NO SOLUTION If there are an infinite number of solutions enter the general solution in terms of x where x is any real number X 10 2x y 2 Y 10y 80 x y 4

Rewrite as sums or differences of logarithms 47 In x y7z 47 In x y z

Express as a single logarithm and simplify if possible log x 2log by 4 log log bx 2log by 4 log x 4 wor uring exponential notation Use integers or fractions for any numbers in the ex

The table below shows the value V of an investment in dollars after n years 3 7 12 14 19 8351 13 9282 72 12368 52 Use your calculator to determine the exponential regression equation that models the set of data above Round the a value to two decimals and round the b value to three decimals Use the indicated variables V Based on the your regression model what is the percent increase per year n 0 V 3600 4321 95 5780 81 V Find V when n 8 Round your answer to two decimal places Interpret your answer by completing the following sentence Be sure to use units in your answer

Express in terms of sums and differences of logarithms 20 16 n log a log a 4 m 9 3 a b 20 16 m n 9 3 a b Uro integers or fractions for any numbers in the expression www

x 4 if x 1 f x 0 OA x 4 if 1 x Ay if 1 x 1 Q OB Ay OU O C Ay Q Q G O D

Shown are the graphs of f x and g x Estimate to nearest integer gof 5

Let P be the plane with equation x 2y 2z 6 Find four distinct points on P at distance 3 10 to the point Q 1 1 3 R1 0 0 0 R2 0 0 0 R3 0 0 0 R4 0 0 0

Jane is fencing in her backyard The yard is a rectangular area where one side is the back of her house The fence will go around only the other 3 sides The side opposite the house is the same length as the house which is 25 feet Jane will use 120 feet of fencing Which equation can Jane use to decide how long each of the other two sides of her fence can be X

Graph the restricted secant function y 4 secx by restricting to the intervals and a Use the horizontal line test to explain why the restricted secant function has an inverse function Use the graph of the restricted secant function to graphy 4 sec a Choose the corect graph below OA 42000 O C a OD TRITTSP

Express as a product log MT 10

a fog b gof c fof d g g a gXx Factor completely Simplify your answer What is the domain off g Select the correct choice below and if necessary fill in the answer box to complete your choice OA The domain is 1 Use a comma to separate answers as needed Use integers or tractions for any numbers in the expression OB The domain is all real numbers 00 Factor completely Simplify your What is the domain of gt Select the correct choice below and if necessary in the answer box to complete your choice OA The domain is Use a comma to separate answers as needed Use integers or fractions for any numbers in the expression OB The domain is all real numbers c Factor completely Simplify your answer What is the domain off Select the comect choice belour and if necessary fil in the answer box to complete your choice OA The domain is Use a comma to separatie answers as needed Use integers or tractions for any numbers in the expression OB The domain is all real numbers d Factor completely Simplify your answer What is the domain of gg Select the correct choice below and if necessary in the answer box to complete your choice OA The domain is Use a comma to separate answers as needed Use integers or fractions for any numbers in the expression Themen CID

Q Use the least Squares method to fit the equation ax by 1 0 to the data X y 0 1 1 1 1 9 2 3 0 3 3 9

Use the tabular representation of f to complete the column for f x 3 4 HA x On 2 3 8 10 f x 1 3 4 x f x 1 00 8 15 12

log 2 0 301 and log a7 0 845 Use these values to evaluate log a98 log 98 a Simplify your answer TH

Graph the following function f x a Choose the correct graph below A Af x 30 6 if 0 x 2 12 if 2 x 4 18 if 4 x 6 24 if 6 x 8 b What type of function is this OA absolute value function OC piecewise step function OB Af x 30 C Af x 30 B piecewise polynomial D power function O D Af x 30 to 10

a Graph f x OA Ay 30 5x 6 b Find f 1 and f 3 c State the domain of the function b f 1 x a Choose the correct graph below if x 2 if x 2 and f 3 B 30 y OU x W Ay 30 D Ay 30

Graph the following function 6 if 0 x 2 12 if 2 x 4 18 if 4 x 6 24 if 6 x 8 f x a Choose the correct graph below OA Af x 30 B Af x 30 10 O C Af x 30 O D Af x 30

y sin 30 Choose the correct graph below OA 1 Ay the sine run OB 14 Ay 1 Q Q ECCCE OC Ay 1 Q Q 5 OD Ay 1 HIN N

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Click here to watch the video a Graph f x O A 6x 9 AY 40 x b Find f 2 and f 4 c State the domain of the function 10 if x 3 a Choose the correct graph below if x 3 B AY 40 AY 10 40 mi 10 O D G 40 Ay 10

The table below gives lawnmower rental rates as a function of the number of hours the lawnmower is rented Write the step function that gives the rent R as a function of the number of hours rented x for 1 5 x 12 Number of hours 1 5 x 3 3 x 6 6 x 9 9 x 12 Rental rate 29 56 34 55 39 54 44 53 R x if 1 5 x 34 55 if X if x if 9 x

Convert to a logarithmic equation 1 36 6 The equation is Use integers or fractions for any numbers in the equ

FORUM DESCRIPTION One Saturday I went to Busch Gardens to ride a new rollar coaster While waiting in line my daughter noticed that part of this coaster resembles the graph of a polynomial function that they studied in a pre calculus class She found that part of the coaster can be modeled by the function below h t 0 21 41 24r 48r Here t is time in seconds and h is height in feet Graph this polynomial in the grid below 110 100

em 13 7 points Find the coordinate vector v where v A 3 4 9 2 B 13 4 9 2 C 3 4 5 2 D 3 4 9 2 E 13 4 5 2 38 and 56 5 B 3 9 SPRI

1 Let W span x X X3 where x 2 x 0 V V2 V3 for W 8 1x a 0 0 Construct an or

2f1 3 TI 3 3 2 B 1 2 3 4 TI 3 2f1 3 Writev never as a fraction in simplert form a b graph

Use the Rational Roots Theorem polynomial division and factoring to completely factor the polynomial f x 2x5 7x 18x 8x 8 List all of the zeros 5 points

10 8 10 8 6 4 2 Slope m 9 4 2 2 4 6 8 10 2 A Find the slope of the line 4 6 8 10

A polar equation is given 20 8 0 0 4 r a Express the polar equation in parametric form x t y t 0 t 4 A polar equation is given r 20 8 0 0 4 a Express the polar equation in parametric form x t y t x osts 4

Find the exact value of the expression cos 2n 9 OA sin OD 3 2 O B O c 1 1 2 18 cos sin 18 2n 9

The equation of the given curve in solid blue is Type an equation using x as the variable Use integers or tractions for any numbers in the expression write an equatuon for the solif blue curve 10 8 6 4 2 2 5A 6 5t 3 15t 2 X 10t 3 Q

A plaza is to be constructed in a city redevelopment area The shaded area shown represents the proposed plaza Determine Zy in the diagram below to the nearest hundredth degree 6000m RADIUS 31 31 Ob 12 30 OC 16 07 Od 41 63 204 0m 162 0m

f x 7x 5x 63x 45 a List all rational zeros that are possible according to the Rational Zero Theorem Choose the correct answer below 1 OA 1 3 9 5 15 45 1 OB 1 7 t 1 3 1 OC 1 17 1 1 7 Im 3 7 3 1 T 10 t 1 6 1 H 1 6 1 7 96 1 1 t H H 115 15 7 5 1 3 9 5 15 77 7 H H 1 OD 1 3 6 5 15 45 t 7 5 7 7 1 1 15 3 6 1 15 1 7 57 7 1 7 15 7 15 1 1 t 45 7 1 45 1 7 45 1 7 t 45 45 15 45 7 7

x 3 9 Piecewise functions Let s try another function f x 0 3 x if x 2 if 2 x 2 if x 2 a Match each function piece with its shape y x 3 y 0 y 3 x b Show what each shape looks like when it is cut off by the given domain Make sure to determine if endpoints should be open circles or closed circles y x 3 if x 2 y 0 if 2 x 2 y 3 x if x

In the diagram rectangles ABCD CEFG and FHJK are congruent Determine the measure of ZAJC A B E J H K

Pick all translations that occurred from the parent function y cosx for the function be y cos x 1 Select one or more up t down 1 left 1 right 1 up 1 left T down T right T

Math Intercepts graphing Follow the steps below to graph the function f x 2x 4x 6 Sect Qu a Recall that if a 0 then the parabola will open up and if a 0 then the parabola will open down Identify a Will the parabola open up or open down b In College Algebra we saw that the vertex of a parabola can be found using the formula f Use the formula to find the vertex of the parabola Step 1 Find the x value x b 2a Step 2 Find the y value f just means to plug your x value you got above into your function to find the y value So take the x value you got and substitute it back in the original function to find the y value of the vertex y 2 4 6 Step 3 Use your x and y values to write the vertex as an ordered pair y intercept c Find the x and y intercepts Write your answers as ordered pairs x intercepts functions Let s try another function d Plot the vertex and intercepts and connect with a smooth curve to graph the function 10 08 61 4 2 10 8 6 4 2 N 4 4690 8 10 24 6 8 10

Consider the following autonomous DE y 4 y 1 2 y 3 Choose all correct answers There are two critical points If y 1 4 then the solution is an increasing function One critical point is semi stable y 3 is a solution One critical point is a repeller If y 0 2 then lim y x 3 X 00 One critical point is an attractor

solve the triangle b 2 c 7 A 100 degree a B degree C degree

Sketch one cycle of the sine curve Assume a 0 Write an equation for the graph amplitude 2 period 4x Choose the correct graph below OA Ay Q EN B A 444 14 Ay Q Q OD Ay hi

Evaluate the integral 1 v 3v ov dv 64 39

For f x 3a 7m find A f a B f a h C find and simplify f a h f a h for h 0

Solve the given equation if we know that x 3 is a solution of the equation x6 4x5 6x 36x 27x 0

Find the amplitude of the sine function y sin 50

60 5 30 t V CD V FIND AD CD AD O st BD 100LB

Express in terms of sums and differences of logarithms 2 3 3x y In In 2 11 A

Find the amplitude of the sine function MA Answer Check