Quadratic equations Questions and Answers

Given the standard form of a parabola y x 4x determine the vertex form of the graph y x 4 y x 2 4 y x 4 y x 2 4

The following parabola is in standard form y x 12x 5 What would need to be put in the space below to complete the square and covert to vertex form y x 12x 36 36 144 144 6 6 12 12 5

Find the graph of the following ellipse Identify the domain range center vertices endpoints of the minor axis and the foci x y 25 16 1 What is the center of the ellipse 0 0 Type an ordered pair Round to the nearest integer as needed Use a comma to separate answers as needed What are the vertices of the ellipse Type an ordered pair Round to the nearest integer as needed Use a comma to separate answers as needed

A one way road passes under an overpass in the shape of half an ellipse 30 ft high at the center and 20 ft wide Assuming a truck is 12 ft wide what is the tallest truck that can pass under the overpass The tallest truck that can pass under the overpass is ft tall 30 f 20 ft

Use the quadratic formula to solve x 3x 1 0 3 5 3 5 2 2 O O 3 13 3 13 2 2 3 5 3 5 2 2 3 13 3 13 3 13 2 2

How is the graph of g x x 1 related to the graph of f x x

91 x9

d 2x 6 8 6 9 2x 3

Use the interactive figure to find your answer Use the left and right arrow keys to move along a slider as needed Click here to launch the interactive figure P Conics Rectangular Form Google Chrome The length of the major axis is Simplify your answer 4 media pearsoncmg com cmg pmmg mml shared precalc ifigs HTML5 1Fig2 20Precalc2 conics Conic Ellipse x h a Parameters a b o y k 6 4 5 1 Conics Rectangular Form 9 8 7 9 8 7 6 5 4 3 2 6 15 4 3 2 4 2 1 ty 1 2 3 4 5 6 7 8

1 A 11 1 a Find a basis for the column space of A b Find a basis for the nullspace of A A 0 11 0 B 1 0 0 0 0 1 0 0 C 1 11 1 0 11 0 D 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 E 1 11 1 0 11 0 1 10 0 F 1 11 1 0 11 0 1 10 0 1 1 1 G 1 1 1 H 1 11 1 Problem 9 a C Problem 9 b 0 1 1 11 14 1 0 1 1 A 1 1 0 1 0 1 B 1 1 0 1 1 0 1 C 1 0 1 D 1 0 E 1 1 0 1 F 1 1 0 1 G 1 1 0 1 1 0 1 H 1 1 0 1 0 Select

Find the graph of the following ellipse Identify the domain range center vertices endpoints of the minor axis and the foci x v 1 25 9 What is the center of the ellipse Type an ordered pair Round to the nearest integer as needed Use a comma to separate answers as needed

4 Graph the image of rectangle STUV after a dilation with a scale factor of 1 centered at the origin V 104 8 9 6 2 U T

Solve for q 16q 2q 139 13q 15

11 2x6 10 13 2 4x 10 15 5 3x 10 12 12 5x 2 14 4 10x 6 16 12 2x 8

Find the angle in degrees between vectors u 8 7 and v 8 3 0

9 3 5 2x 10 1 5

1 5x 24 59 3 1 x 1 2 C Show your work to solve each of the equations below 2 12x 22 26

19 1 5x 3 4 8 4 20 1 2 1 4 1 4 x

15 5 3x 10 17 10 12 x 16 12 2x 8 18 2x

11 2x6 10 13 2 4x 10 Practice No Calcul 12 12 5x 2 11 1

5 2 4x 2 8 8 4 16 7 1 2 X x 1500 9 3 2x A 5 6 10 2x 12 8 4x 2 24 10 1 2 x 8 x

5 2 4x 2 8 8 4 7 26 1 x 16 6 10 2x 12 8 4x 12 24 2

10 Graph each of the following equations using the method indicated a Use the slope and y intercept b Use a point and the slope 2x 3y 9 0 y 5 2 3 x 4 10 8 642 10 8 4 1 21 2 14 6 6 48 10 2 6 8 10 10 8 6 4 2 10 8 6 4 2 2 8 10 3 6 8 10 c Use the x and y intercepts x 5y 10 22 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 2 6 8 10

7 a Write an equation in general form for this line 4 2 4 2 0 X b Rewrite the equation in part a into slope intercept form What is the y intercept of this line

Problems Be sure to show all work for each of the following questions You must include all formulas 6 Graph the line with y intercept 5 and slope 4 Write the equation of this line in slope intercept form MATUR 10 8 6 4 2 L B 6 4 Lo 2 2 4 6 00 201 6 8 10

5 Write this equation in slope intercept form y 8 x 2 1 C y X a b 38 5 8 38 y 5x 5 38 5 1 38 y x 5 5 y 1 d y x 3 7 y mx b

a b an equation to describe this graph 2 0 2 2 y x 3 2 y 3x 3 X C d 2 5 2 5 y x 3 y x 3

3 To join a tennis club Josephine pays a start up fee of 125 plus a monthly fee of 16 Write an equation to represent the total cost C dollars for t months of membership a t 16C 125 c b C 16t 125 d 4 Determine the slope and y intercept of this graph C 16t 125 C 125t 16

11 Determine the slope of this line segment Determine the y intercept Write an equation for the line 23 12 2 62 68 3 2 1 10 1 2 3 4 5 6 1 2 3 5 5 6 2 m b Equation y 3x 6 y 1 2 x x 2

1 Write an equation for the graph of a linear function that has slope and y intercept 7 b y x y x 7 C d y x 7 y 7x

12 a Graph the line with y intercept I and slope 2 3 Include a minimum of three points m 213 b 1 b Write an equation for this line in slope intercept form y 2 22 1

5 Determine the slope of the line that is parallel to this line a 73 b 7 7 C 3 7 d NIM segment X

A 3 Is the slope of this line segment positive negative zero or not defined a zero b positive B8 C not defined d negative 4 Is the slope of this line segment positive negative zero or not defined 8 44 Ty 0 94 y mx b X

Ex 7 Write an equation of the line in general form that is parallel to the line y 3x 5 and passes through the point 6 5 m 3

Ex 6 Write an equation for the line with a slope of 3 4 and an y intercept of 6 Give your answer in general form y 4 9 4 3 X 46 14 m 44 4 y 47 3x 24

M Ex 4 Write an equation for the line with slope of 2 3 and passing through the point 1 4 Answer in general form

Ex 3 Rewrite this equation in general form y 3 4 x 2 8 4X 747 4 3 sts

Ex 2 Rewrite this equation in general form y 1 2x 7

1 f x 4x 2 Find f 0

Find each product 5 3a 7a 1 a a 1 A 3a 10a 9a 6a 1 B 3a 7a 1 4 C 3a 4a 5a 8a 1 D 8a 36a 12a 24a 32

Enter the system of equations that is represented by the augmented matrix below Use x y and z for the first second and third variables respectively You do not need to solve the system Equation 1 Equation 2 Equation 3 3 5 7 2 6 2 0 4 1 4 4 2

To enter a matrix type each row as a comma separated list pressing Enter when you need to create a new row You don t need to enter parentheses or brackets Enter the matrix below 8 6 4 6 02

Use the leading coefficient test to determine whether y o or y o as x for the function y 2x x 16 As x y

Multiply and simplify your answer State any restrictions on the domain 62 36 4 6 12 b b X 6 2 LIST FACTORS FROM LEAST TO GREATEST LIST RESTRICTIONS FROM LEAST TO GREATEST

Multiply and simplify your answer State any restrictions on the domain 3x 27 x 13x 36 4x 16 X X LIST RESTRICTIONS FROM LEAST TO GREATEST

Find the vertical and horizontal asymptotes of f x 6 Remember to write the asymptotes as equations and do not type spaces in your answers Vertical asymptotes Horizontal asymptote POSSIBLE POINTS 1 and

S varies inversely as G If S is 3 when G is 0 4 find S when G is 2 a Write the variation Find S when G is 2 a How are these two variables related OA S KG B S kG C O D k S G S 2

Simplify and state any restrictions on the domain 3 15 54 az

Pairs of markings a set distance apart are made on highways so that police can detect drivers exceeding the speed limit Over a fixed distance the speed R varies inversely with the time T In one particular pair of markings R is 44 mph when T is 5 seconds Find the speed of a car that travels the given distance in 4 seconds R mph Round to the nearest whole number

Graph the function f x Identify the domain the range the horizontal asymptote and the vertical asymptote Domain i Range i Horizontal Asymptote Vertical Asymptote i POSSIBLE POINTS