Quadratic equations Questions and Answers

The owners of a circus are planning a new act They want to have a trapeze artist catch another acrobat in mid air as the second performer comes into the main tent on a zip line If the path of the trapeze can be modeled by the parabola y x 16 and the path of the zip line can be modeled by y 2x 12 at what point can the trapeze artist grab the second acrobat Above are two trapeze artists catching each other in midair In this new act a person on a zipline will glide right through which for timing essential

Graph the circle by rewriting the equation in standard form x y 4x 4y 1 0 1 Ty 6 65 5 4 3 2 1 N 3 4 5 1 2 3 4 10 8

x y 7 x y 7 2

linear quadratic system algebraically Solve the given y x 2x 4 y 2x 4

Ty 5 6 5 4 3 2 1 000 3 2 1 1 2 3 4 2 3 4 5 7 Which of the following points is on the circle centered at 8 9 with a radius of 10 unit A 0 3 B 3 5 C 9 1

6 5 N W 3 2 6 5 4 3 2 1 1 1 2 3 4 5 1 2 3 4 5 6 X 1 What are the coordinates of the circle s center 2 What is the radius of the circle T 3 Given the circle the equation of the circle in standard form D

Determine if the point P 3 6 is on a circle centered at 1 3 with a radius of 5 units

T 31 K L J O INJ 4 10 1 IND J 14 6 1 What are the coordinates of the circle s center 2 What is the radius of the circle 3 Given the circle write the equation of the circle in standard form

Not 0 6 Which of the following points is on a circle centered at 5 1 with a radius of 6 4 2 3 0 1 1 1 5

Determine if the point P 1 4 is on a circle centered at 2 3 with a radius of 2 units

The circle with center C 2 5 and containing the point P 2 1

Write the equation of the circle The circle with center C 1 4 and radius r 2

Here is a graph of the function f 3 2 1 W 24 5 Use the graph to find the following If there is more than one answer separate them with comma a All values at which fhas a local maximum b All local maximum values of f

Determine which quadratic equation has tw non real solutions A 2x 12x 18 0 B x 5x 3 0 C 3x 3x 2 0 D 2x 16x 2 0

What is the value of n in the equation 2n 4n 6 0

Determine which quadratic equations hav 1 real solution Select two that apply 9x 8x 8 0 x 4x 4 0 10x x 9 0 3x 6x 3 0

Which of the following values of x are solutions to the equation x 2x 3 Select all that apply A 1 4i B 1 4i D 3 DE 5

Which is the value of n in the equation n 6n 25

Solve the equation by completing the square State whether the solutions are real or non real x 8x 17 0

Solve the equation by completing the square State whether the solutions are real or non re x2 10x 7 0

Find the type of and the number of solutions for each equation Hint Use the discriminant 2x 3x 2 0

Find the type of and the number of solutions for each equation Hint Use the discriminant 3x 2x 6 0

Identify the number of x intercepts and the number of real number solutions for the following quadratic equations

Identify the number of x intercepts and the number of real number solutions for the following quadratic equation N 4 0 2 Het X 6

In Exercises 5 18 solve the equation using the Quadratic Formula Use a graphing calculator to check your solution s See Examples 1 2 and 3 5 2 4x 3 0 6 3x 6x 3 0 7 6x 15 0 8 6 2x 1 0 In Exercises 19 26 find the discriminant of the quadratic equation and describe the number and type of solutions of the equation See Example 4 19 x 12x 36 0 20 2 x 6 0 21 4n 4n 24 0 22 2x 12 0

T 77 212 5 27 erlio 3

nd the indicated term for the geometric sequence 9 9 9 024 256 64 3 the 8th term The 8th term of the g

0 1717171717 The fractional notation for 0 1717171717 is Simplify your answer Type a fraction Q

CC Cosex 8sinxsin3 cos3x COSX complete solution

A theater has 34 rows of seats The first row has 22 seats the second row has 26 seats the third row has 30 seats and so on How many seats are in the theater The theater has seats

Find the indicated term for the geometric sequence 8 8 8 243 81 27 the 10th term The 10th term of the geometric s

Find the sum of the first 10 terms of the geometric series 4 8 16 The sum of the first 10 terms of the geometric series is Simplify your answer

Find the common ratio for the following geometric sequence 5 20 80 320 The common ratio is Simplify your answer Type an integer or a

Find the common ratio 4 3 8 16 3 3 32 3 The common ratio is Type an integer or a simplified fraction

theater has 34 rows of seats The first row has 22 seats the second row has 26 seats the third row has 30 seats and so on How many seats are in the th he theater has seats

Write a formula for the general term the nth term of the arithmetic sequence below Then use the formula for an to find a2o the 20th term 1 4 10 16 22 The formula is a 7 Simplify your answer

Find the sum of the first 65 terms of the arithmetic series 22 24 26 28 S65

8 10 Divide 8 11x 57x 21x 27 11x A x 6x 3 B x 6x 5 C x 6x 4 D x 6x 6 1 11x 9 5 11x 9 9 Find each product 10 3p p 8 4p 7p 5 A 12p 17p 54p 51p 40 B 12p 25p 40p 61p 40 C 12p 17p 54p 51p 40 D 12p 7p 40 9 9 8x 57x 33x 5 8x 1 A x 7x 5 B x 5x 3 C x 7x 8 D x 5x 2 State if the given binomial is a factor of the given polynomial 11 11 4x 24x 5x 27 x 6 12 A No B Yes 1 8x1 4 8x 1 12 x 8 7x 7 x A Yes B No

4 6 Simplify each sum 4 2x 5 6 2x A 1 C 1 5x 6 A Simplify Your answer should contain only positive exponents 7 C 26 a 2a b 10 16a lo B 1 x D 3 5x B D 64 16a 10 5 64g 12 b 5 2x 6x 3x x A 7x x C 8x x 7 2ab a b a b 2 4b A C 64gH B D B 15x D 14x 166 20

4 6 REVIEW REVIEW Simplify each difference 2 3n 6 3n 4n 7 7n A n 4n 12 6n B n 4n 14 6n C n 4n 12 D n 4n 13 Simplify each sum 4 2x 5 6 2r A 1 C 1 5x 6 A 266 a 1 16a 10 B B 1 x D 3 5x Simplify Your answer should contain only positive exponents ab 2a b 2a 7 2ab D 6 10 5 16a 64 2 3 7 3 6n 5 2n 4 5 8mm A 10n 7n 5 B 10n 8n 5 C 10n 2n 5 D 10m 2n 5 2x 6x 3x x A 7x x 2 C 8x x reserved A 4b C 64a D B 15x x D 14 8b 166

Let f x z 1 g x 7 3x x2 and h x 2x 1 Match the following function operations f g z hf x 4 g f x h g x 3z 6 2x 2 2x 1 I II II

Let f 2 x x 6x 1 and g x 9 2 Determine 3f x 2g r In the space provided type the coefficients of your final solution in arx bx c form 3f x 2g x

Match each function from the left with its inverse from the right f x x 4 f x x 4 4 C f x 3x 2 f x 2x 3 x f 1 x f 1 x 13 x X T x x 1 2 x T wo 100 8 3 CO 6 2 3 3 2

Choose the graph that does NOT represent a function and its inverse In each graph the dotted line represents the line y x A B 5 4 3 2 5 4 3 2 1 1 2 1 21 3 4 1 2 3 4 5 1 2 3 4 5 C D 2 5 4 3 2 1 1 2 5 4 3 2 1 5 2 3 4 1 2 3 5 1 2 3 4 5 Review

Place the following steps into the correct order for algebraically finding the inverse of a function Solve for y in terms of x Set the function equal to y Swap x and y Next

3 Consider the angle 0 4 a 2 points To which quadrant does belong Write your answer as a numerical value b 4 points Find the reference angle for in radians c 4 points Find the point where intersects the unit circle

Find the area of the shaded region 2x 3 1 3x 2 4x 5 x 81 Type a response zoom in Write an expression that represents the area that is shaded 1

Divide 8 91x 43x 17x 5 13x 5 A 7x 6x 1 B 7x 6x 3 C 7x 6x 3 D 7x 6x 1 13x 5 5 13x 5 3 13x 5 Find each product 10 4a 3a 4 4a 3a 8 A 16a 9a 32 B 16a24a 25a 12a 32 C 16a 7a 36a 32 D 16a 24a 25a 12a 32

3 2 4x 8x 3x 6x O O O O 7x 14x 12x 14x 3 4x 14x 21x 0

A DJ is preparing a playlist of 21 songs How many different ways can the DJ arrange the first six songs on the playlist There are different ways that the DJ can arrange the first six songs on the playlist Type a whole number