Quadratic equations Questions and Answers

8 9 points Match each of the three given graphs to the one function that is MOST LIKELY the one with the given graph Look at the DEGREE and the LEADING COEFFICIENTS as well as what is happening at the x intercepts Simply write the letter of the function on the line under the matching graph ONLY ONE function will go with each graph thus TWO of the functions will NOT be used at all a x ax x 3 x 1 for a 0 b f x ax 2x 3x 4 for a 0 c f x a x 3 x 1 for a 0 d f x ax 2x 3x 4 for a 0 e f x a x 2 x 0 5 x 1 5 for a 0 y 10 4 pdf 5 2 1 5 1 0 5 0 5 1 1 5 2 2 6 8 10 8692 x 4 40 20 A 20 100 0 100 200 300 X

4 10 points The profit that the vendor makes per day by selling x pretzels is given by the function P x 0 004 x 2 8x 300 A Find the number of pretzels that must be sold to maximize the daily profit

1 8 points Sketch the graph of y x 3 2 using transformations be sure to label the vertex

3 10 points Write an equation for the parabola given below in vertex form i e y a x h k 1 2

The sales at your high school basketball game vary directly with the number of attending If the sales for a game are 3200 when 800 people attend determine how many people attend if the sales for a game are 2200 What does the constant of variation represent in this problem The demand of Starbuck s coffee is inversely related to the price Which means as the price of the coffee goes the demand will go Sketch a graph to represent this relationship and properly label the x and y axis

7 In economics revenue R is defined as the amount of money received from the sale of a product and is equal to the unit selling price p of the product times the number x of units actually sold That is R xp The Law of Demand states that p and x are related As one increases the other decreases Suppose that p and x are related by the following demand equation A Express the revenue R as a function of p x 4p 100 0 p 25 B What is the revenue if 18 units are sold c Sketch the graph of the revenue function D What quantity x maximizes revenue what is the maximum revenue 700 600 500 400 Revenue dollars 300 200 100 4 8 Price dollars 12 16 20 24

Simplify 5 2b ba 2a b4 A 4b4a8 C 4a6b6 B 16ba D 4b6a6

Integer Exponents Simplify 1 3p 3p 2p A 6p C 6p B 4p5 D 18p8 L

8 105 4 10

a Graph the function by dragging each of the following to a correct position the vertical asymptote a first point a second point 15 f x log x 3 2 10 5 15 10 0 0 5 0 5 1 1 1 1 A 5 LO 10 I C 15

Convert each logarithmic equation into its equivalent exponential form You do not need to find the value of any variables a log3 243 5 Exponential equation b log5 25 2 Exponential equation c log4 a 2 Exponential equation d log 11 y Exponential equation

Identify the missing number by using logarithms and a calculator Round answers to 3 decimal places a 8 29 b 10 28 c e 45 d 6 1

Identify the missing number without using a calculator If no number makes the statement true enter DNE a log4 64 b logs 64 c log3 81 d In es e log 100000000

For each function below find the indicated inverse function Be mindful of the following when using Derivita To enter a log of any base type log b base argument log argument defaults to the base 10 In argument is the natural log which has base e a f x 7 b g x c h x 10 h y d m x e m y

Identify the missing number without using a calculator If no number makes the statement true enter DNE a 2 8 b 6 36 c 2 16 d e e5 e 10 1000000

Determine the value of y for each of the following Recall that the base and argument of a logarithm must both be positive a log 25 2 b logs y 1 y c log4 64 y

Find the exact acute angle 0 for the given function value tan 0 1

Carmen s fixed expenses are the following Los gastos fijos de Carmen son los siguientes rent cable TV Health club loan car loan car insurance 700 45 25 100 129 100 When rounding to the nearest 10 her fixed expenses are Al redondear a los 10 m s cercanos sus gastos fijos son

9 The quadratic function has a domain of 0 00 and a range of 0 0 10 The absolute value function only has an interval of increase 11 The linear equation function has a local minimum 12 The following ordered pairs represents a function 2 3 1 5 1 7 0 9 1 11 13 The end behavior of the quadratic function is as x 00 f x 0 and as x o f x 14 The end behavior of the linear function is as x f x and as x f x B 15 The x intercept for the linear absolute value and quadratic function is 0 Mentify if the following statements are True or False

10 The graph of a piecewise function g is shown in the xy plane for 7 x 6 Write the equation for g 74 6 5 4 3 2 1 6 5 4 3 2 1 0 1 2 3 4 5 67 2 3 4 5 6 7 tx

29 Write an equation in slope intercept form for the line containing the points 0 13 and 4 11 30 Evaluate 16 15 5 3 5 2

tch the transformations 2 3 8 4 7 5 6 with the correct equation Horizontal shift left Horizontal shift right dentify if the fallow Vertical shift up Vertical shift down Reflection across the x axis Reflection across the y axis Vertical stretch Vertical compression A y f x B y f x m C y f x m D y m f x m 1 E y f x m F y f x G y m f x 0 m 1 H y f x m

26 Match each of the following functions with the the graph that best describes the situation a The temperature of a bowl of soup as a function of time b The population of Africa as a function of time c The height of a golf ball hit by a 5 iron as a function of time 1 11 III

9 3 4 B 10 5 6 10 ys x 5 8 zoom in 9 10 11 10 SHAD

mative com formatives 63580800 1 Sketch the graph of each linear inequality 1 y2x 3 A B D 2 2 5x y S s A B D 13 1

Solve the equation by graphing x 14x 49 0 First graph the associated parabola by plotting the vertex and four additional points two on each side of the vertex Then use the graph to give the solution s to the equation If there is more than one solution separate them with commas 30 B Ho 6 X Solution s x 0 DO No solution X 03

B 3 4 44 Y 7 y x 2 5 y 2x 6 7 8 B 11 Show the solution to the following system FOLLOW D 9 10

Use the ALEKS graphing calculator to find all the real zeros of the quadratic function f x 3x 2x 2 Round to the nearest hundredth If there is more than one answer separate them with commas If there are no real zeros click on None real zero s 0 0 None

A 4 1 C 1 4 Sketch the solution to each system of inequalities 7 y x y2 2x 3 B D r 2 B A P B 4 D 1 4 AN 100 Y C2822 Kule Software LLC All sighis roser cel A 7 5 C 7 10 8 2x 3y2 3 x 3y 6 A B O D 4 2 Made with 17 222 Inti a ste B 7 8 D 1 6 Algebre 2

g x x Plot five points on the graph of the function one point with x 0 two points with negative x values and two points with positive x values Then click on the graph a function button 32 EG 21x 10 8 13 10 X

Evaluate each expression using the values given in the table 1 0 2 3 1 6 0 1 27 X f x g x a fog 1 d gof 0 3 9 7 a fog 1 1 b fog 1 1 c gof 1 7 d gof 0 2 6 2 b fog 1 e gog 2 1 3 0 3 9 c gof 1 f fof 1

Divide the following polynomials using any method of your choosing 2 16x 3 x 4 11 x x 4

Use the graphs for f x and g x to evaluate the expressions below Write your answer as a whole number or a reduced fraction 6 5 4 3 2 1 1 f x 2 1 f 3 g 1 f 3 g 5 CA A 10 X 160 16 5 4 3 2 1 g x 1 1 g 5 f 4 g 1 f 4 2 st X 160

6 end 10th tem The end 8 sequence o the b the third is 39 tem of sun of 230 Find is the first tem of sum of the an the the first arithmetic sequence first to terms sequence 13 terms is of the 416

Divide the following polynomials using any method of your choosing 2x 7x 2x 9 2x 3 2 x 2x 3

the linear programming problem nimize and maximize 10x 30y bject to 2x y 2 48 x y 232 x 2y 40 xyzo Select the correct choice below and fill in any answer boxes pr your choice What is the minimum value of 2 OA Type an integer or a fraction OB There is no minimum value of z

1 2 44 9 D 3 ys 33 2 4 A 10 5 6 10 5 J 8 7 8 A zoom in 9

1 point Let f x be the function 3x2 2x 2 Then the difference quotient f 2 h f 2 can be simplified to ah b for 2 h 2 a and b

Please give complete well written solutions to the following exercises and submit via Gradescope 1 2 points Sketch the regions of integration for each iterated integral below and write each as an iterated integral in the opposite order You may need to break the integral into a sum of 2 iterated integrals a b r5 clnx f x y dy dr 4x 5 f x y dy dx

K Write the expression as a function of x with no angle measure involved 5 55 6 sin 5 sin 5 0 X 6 Simplify your answer including any radicals Use integers or fractions for any num

K Use a sum or difference formula to find the exact value of the trigonometric function sin 11x 12 11T sin 12 Simplify your answer including any radicals Use integers or fractions for any numbers in the

In 1 8 match each expression with the correct choice to form an identity Choices may be used once more than once or not at all sin x sin x 1 cos x y 2 cos x y Drag each of the expressions given above into the appropriate area below 3 cos 4 sin 5 cos 6 sin 7 tan 8 cot 7 IN COS X cos x cosy sin x sin y cos x cos y sin x sin y sin x cOS X sin x tan x cos x cos y sin x sin y cotx COS X cotx tan x COS X Question 1 5 3 1 8 cos x cos y sin x sin y

K Find the exact value of the expression by using appropriate identities Do not us sin 84 cos 39 cos 84 sin 39 sin 84 cos 39 cos 84 sin 39 Type a fraction

Write the expression in terms of sine and cosine and simplify so that no quotients appear in the final ex all functions are of 0 only sin 0 sec 0 cot 0 sin 0 sec 0 cot

1 The following exponential function is a transformation of the original function f x 5 Give the following details g x 52 3 1 a g x is a reflection of f x about the axis b The graph of the function is behavior c g x is f x shifted unit s d g x is f x shifted unit s e The transformation of the original point 0 1 on f x is now at f The domain of g x is g The range of g x is from left to right according to g x

Part 1 of 2 Use synthetic division and the factor theorem to determine whether x 4 is a factor of f x f x 3x3 15x2 16x 16 Complete the first row of the synthetic division table

For the given polynomial P x and the given c use the remainder theorem to find P c P x 3x 5x 7x 3 5 P c Simplify your answer www

4 12 y x 1 3 V 3 432 2

10 y 2x 2 y2 x 3 4 3 2 1 ZO

4 2x y 3 4x y 3 A B D 4 AV H A V x X x N