Savas Realize Algebra

Algebra 2 Topic 2 Review

What is the equation in vertex

form of a parabola with a vertex of

(3, −2) that passes through (5, −1)?

.

Multiple Choice

What is the equation written in vertex form of a parabola with a vertex of (–5, –4) that passes through (–7, 8)?

• y = (x + 5)² – 4

• y = 3(x + 5)² – 4

• y = 3(x + 7)² + 8

• y = (x – 5)² – 4

What is the vertex of the graph of

the function f(x) = x² + 8x?

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Multiple Choice

What is the vertex of the graph of the function f(x) = x² + 10?

• (0, 10)

• (10, 0)

• (−10, 0)

• (0, −10)

The path of a projectile launched from a 20-ft-tall tower is modeled by the equation y=−16x² + 32x+20. Graph the equation. What is the maximum height, in feet, reached by the projectile?

Multiple Choice

The path of a projectile launched from the top of a 10-ft-tall tower is modeled by the equation y = –16t² + 32t + 10. Which is the correct graph of the equation?

Multiple Choice

The path of a projectile launched from the top of a 10-ft-tall tower is modeled by the equation y = –16t² + 32t + 10. What is the maximum height?

• 10

• 32

• 26

• 27

Solve the equation x² − 18x = 40.

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Multiple Choice

Solve the equation

x²+ 7x=18.

• x = -9, 2

• x = 3, -6

• x = -2, -9

• x = -3, 6

A ball is thrown from the top row of seats in a stadium. The function 

h(t) = –16t² + 16t + 96 gives the height, h, in feet, of the ball t seconds after it is thrown. How long will it be before the ball hits the ground?

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Multiple Choice

A ball is thrown from the top row of seats in a stadium. The function h(t) =−16t²+ 80t+ 96 gives the height, in feet, of the ball t seconds after it is thrown. How long will it be before the ball hits the ground?

• 6

• -1

• 96

Use square roots to solve the equation x² = –100 over the complex numbers.

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Multiple Select

Use square roots to solve the equation x² = −121 over the complex numbers. Select all that apply.

• 11

• -11

• 11 i

• -11 i

Solve 0 = x² + 8x + 17 by completing the square.

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Multiple Choice

Solve 0 =x²+ 2x + 10 by

completing the square.

• x= -1-9i, -1+9i

• x=-1+3i, -1-3i

• x=4, 2

• $$x=\sqrt{10}-1,\ -\sqrt{10}-1$$

Solve x²+ 5x+ 8 = 0 using the

Quadratic Formula.

.

Multiple Choice

Solve x2 + 2x + 4 = 0 using the Quadratic Formula. Select any solutions that apply.

• 
  

  $$x=-1-i\sqrt{3}$$

• $$x=-1-\sqrt{3}$$

• $$x=-1+i\sqrt{3}$$

• $$x=-1+\sqrt{3}$$

A toy cannonball is launched from a cannon on top of a platform. The equation h(t) =−5t²+ 15t+ 10 gives the height h, in meters, of the ball t seconds after it is launched. What equation can be used to tell whether the ball reaches a height of 24 m? Does the ball reach a height of 24 m?

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Multiple Choice

A toy cannon ball is launched from a cannon on top of a platform. The equation h(t) = –5t2 + 30t + 8 gives the height h, in meters, of the ball t seconds after it is launched. What equation can be used to tell whether the ball reaches a height of 34 m?

• –5t² + 30t + 8 = 0

• –5t² + 30t + 8 = 34

• –5t² + 30t + 4 + 34 = 0

• –5t² + 30t + 4 = t + 34

Multiple Choice

A toy cannon ball is launched from a cannon on top of a platform. The equation h(t) = –5t² + 30t + 8 gives the height h, in meters, of the ball t seconds after it is launched. Does the ball reach a height of 34 m?

• yes

• no

Determine the number of real solutions of the system
 $y=x^{2\ }-4$  
 $y=-x-5$  

Multiple Choice

Determine the number of real solutions of the system

$$y=x^2+1$$  
$$y=1$$  

• 0

• 1

• 2

• 3

Solve −3x²− 6x+ 21 = 6x+ 8 by writing a linear-quadratic system and solving using the intersection feature of a graphing calculator

Multiple Choice

Solve the equation 5x² +3x – 14 = –1/3x + 4 by writing a linear-quadratic system and solving using the intersection feature of a graphing calculator. Round to the nearest hundredth.

• x ≈ –2.26 and x ≈ 1.59

• x ≈ –2.63 and x ≈ 4.21

• x ≈ –1.11 and x ≈ 2.11

• x ≈ –2.61 and x ≈ 0.42