Coordinate system Questions and Answers

Identify the vertex and axis of symmetry 7 6 5 4 3 2 Vertex 471 31 1 1 2 3 Axis of Symm

a The sign of the x coordinate is changed Complete list of Hdots

Point U lies on ST such that SU TU is 2 5 Graph U 204 1 8 16 14 N 1 2 10 8 6 4 2 S 27 4 6 8 10 12 14 16 T 18 20 X

3 Identify the shape of the parametric curve defined by the equations t 3 10 st 0 7 0 t 4 3 4 1 8 t 15 8 t 18 Square Rectangle Circle Ellipse and x 3 10 st 0 t 1 0 ts4 1 5 4 t 8 7 8 t 18

CD has endpoints C 3 4 and D 13 15 Point E divides CD into two parts with lengths in a ratio of 1 4 What are the two possible locations of E 10 11 5 6 2 5 5 6 75 8 9 5 3 2 3 8 11 12 8

Point V lies on TU such that TV UV is 3 4 Graph V 104 10 8 6 4 2 T 8 6 4 2 2 4 6 8 10 10 2 6 U 00 8 X 10

each other Use your Convert each angle from radian measure to degrees 7 28 29 8 27 3TT 2 TT 6 30 7 T 9 Complete the table to find the angle me

1 point Find the values of constants a b and c so that the graph of y 1 5 a 8 x a ba c has a local minimum at x 8 and a local maximum at

3 On a standard summer day in upstate New York the temperature outside can be modeled using the sinusoidal equation O t 11cos 71 where represents the number of hours since the peak TU 12 temperature for the day a Sketch a graph of this function on the axes below for one day O degrees F 90 b For 0 t 24 graphically determine all points in time when the outside temperature is equal to 75 degrees Round your answers to the nearest tenth of an hour

person standing on the Earth varies with the time 4 The percentage of the moon s surface that is visible to since the moon was full The moon passes through a full cycle in 28 days from full moon to full moon The maximum percentage of the moon s surface that is visible is 50 Determine an equation in the form P Acos Bt C for the percentage of the surface that is visible P as a function of the number of days t since the moon was full Show the work that leads to the values of A B and C

The coordinates of the endpoints of JK are J 3 4 and K 9 4 Point L is on JK and divides it such that JL KL is 3 1 What are the coordinates of L Write your answers as integers or decimals

A line passes through a circle at point P 5 13 Sketch and label a diagram

does there exist a function which satisfies f x 2 x 1 for all real numbers

The line given by y 1 is dilated by a scale factor centered at the origin The image of the line after dilation is given by y 5 What is the scale factor of the dilation

the cubic pthe cubic parent function was flipped over the y axis the cubic parent function was shrunk vertically by a factor of 1 4 and shifted down 2 units the cubic parent function was shifteleft 5 units up 4 units

1 3 points Find the formula of a function whose graph is transformaed from the function f x x in the following order translated to the left by 4 untis reflected across the x axis and shifted upward by 5 units 2 3 points Identify the transformations of the graph of f x x in order to get the graph of x 2 8 3 4 points Given the graph of f x as follows draw the graph of f x 3 1 TY f x X

If two parallel lines are cut by a transversal which is not true Select one a Supplementary angles are congruent b Alternate interior angles are congruent c Alternate exterior angles are congruent Corresponding angles are congruent d

Lacey made a scale drawing of the middle school The scale of the drawing was 5 inches 2 feet If the gym is 170 inches wide in the drawing how wide is the actual gym Write the number only

Polygon R is a scaled copy of polygon Q What is the value of x Write the number only 14 6 16 Polygon Q P 7 Polygon R

2 Below is your classmate s reference triangle for 7 There is one mistake in their graph Identify 4 mistake and explain what they should remember for next time no woled 180 201 90 W2 00 2 2 45 1 2 2 0 360

1 Draw the reference triangles f r Label the axes Draw the initial and terminal side Label the reference angle in degrees Draw the reference triangle Annotate all sides of the triangle 135 7 4 ge OD Ela 4 rad 225 way villqmia od bortam Sves 201AJUA UOY 320 TOM GO

What angle in the first quadrant could you reference to help you find the sine and cosine of each of the following angles a 330 b 120 c 113 d 203

5 Determine the value for x such that the points A 1 3 4 B 2 3 1 and c 5 6 x all line on a plane that contains the origin

Use a trigonometric ratio to solve for d Round to two decimal places as necessary d Show your work here 24 61

In circle N chord CD is 18 Find the length of the radius to the nearest tenth N D B

Onstruct using only a straight edge and compass a concentric circle same center with the the ameter of the inner circle the circle given below

no ma what as you drag the quadrilateral around What to measure AC 8 9 AE 4 45 EC 4 45 Not Always True All four sides are congruent Diagonals bisect interior angles Sum of all angles equals 360 Diagonal lengths Diagonals intersect at a right angle BD 6 74 After exploring for a while determine which of the following properties are always true by dragging them to the right B BE 3 37 ED 3 37 Always True Opposite angles are congruent Opposite sides are congruent Opposite sides are parallel

Ilhes in the picture below B A E D Rays EA EB E E Lines ED BE Rays EA EC Lines ED BE EA EC Rays EA EC Lines ED BE Rays EA EB E E DE BE Lines ED BE

Finish the proof of the Law of Sines in the case where the points A and D are on opposite sides of BC C A b D a 3 C Figure 3 10 B

Find the arc lengths of the curve r t 11 sin 3t 2 10 cos 3t 9 cos 3t for Ost Answer exactly or round to 3 decimal places

20 Which of the following expressions is equivalent to x 7 A B C V 1 x 7 V x 7 5 x 7 4 14 H D x 7 4

19 Multiply and then simplify the followin 5 10 50 B 25 2 C 5 2 D 2 5 A

5 Olivia solves an equation using the quadratic formula One step of her work is shown 4 16 4 1 6 2 1 Which quadratic equation could this formula represent y x 4x 6 y x 4x 6 y 6x 4x 1 Dy 6x 4x 1

2 Which statement about the function f x x 4 x 3 x 18 As z 0 f z oo and the function has zeros at z 18 4 3 As zoo f z oo and the function has zeros at 18 B C D is correct 4 3 As I 0 f 1 oo and the function has zeros at z 18 4 3 As z o f z 00 and the function has zeros at z 18 4 3

3 Sketch a 270 angle include its initial and terminal side

2 a What quadrant would 4 a I b C d II III IV 3 end up in b What would its reference angle be

Plot the points A 2 3 B 4 8 C 10 1 on the coordinate axes below State the coordinates of point D such that A B C and D would form a parallelogram Plotting point D is optional Click on the graph to plot a point Click a point to delete it A

A C 4 C C A A Bell Ringer Find Slope from Two Points 4 Questions 1 Find the slope of the line that passes through 2 4 and 6 12 2 1 2 2 0 2 Find the slope of the line that passes through 2 8 and 0 8 undefined A 2 11 D 21 B 14 10 D B 3 Find the slope of the line that passes through 5 10 and 5 4 D DATE D Find the slope of the line that passes through 4 7 and 6 4 B 1 2 2 B 0 2 1 2 10 14 13 2

Which of these is equal to cos 8 A cos 82 B sin 72 C cos 72 D sin 82

Find the volume of the oblique pyramid with a square base 104 0 40 85

BD is the altitude to the hypotenuse of right triangle ABC If AB 4 and DC 6 find AD

After rotating figure ABCD 90 degrees clockwise around the origin what are the new coordinates for point C O 2 4 O 0 3 O 4 2 0 3 5 5 A B D IU 5

1 165 9 yd

If mCWZ 228 and mVT 40 find m VPT C W T P V Z

What is the product of the solutions to y 4 y 0 3 0 A 1 2 B 3 7 C 3 7 D 1 2

2 To determine the distance between two points on the coordinate plane begin by connecting the two points Then draw a vertical line through one of the points and a horizontal line through the other point The intersection of the vertical and horizontal lines forms a right triangle to which the Pythagorean theorem can be applied To verify if a triangle is a right triangle use the converse of the Pythagorean theorem Problem Set For each of the Problems 1 4 determine the distance between points A and B on the coordinate plane Round your answer to the tenths place 1 11 12 A 14

Click on the graph to plot a point Click a point to delete it 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 2 1 1 2 3 4 5 6 7 8 1 2 32 4 5 6 7 8 9 10

The scatterplot below shows the number of soft drinks sold in thousands of gallons by fast food restaurants over a 15 year period Soft Drinks Sold thousands of gallons Soft Drinks Sold by Fast Food Restaurants y agur 480 460 440 420 400 380 360 340 320 300 0 2 4 4x T 8 10 12 14 16 6 Time years Of the following equations which best models the ata in the scatterplot y 2 138x2 38 44x 483 27 y 2 138x 38 44x 483 27 y 2 138x 38 44x 483 27 y 2 138x 38 44x 483 27

The first curve representing the function f of x extends along the first quadrant and passes through the points 0 0 4 2 and 7 2 5 The second curve representing the function h of x extends along the first and second quadrants and passes through the points negative 4 0 negative 3 1 0 2 and 5 3

4x 5x k In the equation above k is a constant If the equation has two real solutions which of the following could be the value of k A 4 B 3