get ready for algebra ii - photomath · tion y = 400(.85)2x −6 question 9. the graph of the...

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Get ready for Algebra II

Practice important Algebra II concepts with these advanced problems. In some cases, you will need to apply multiple math concepts to determine the best or most

appropriate solution format. Full solutions are at the end for your reference.

Good luck!

Question 1. What is the slope of the graph of the equation?

Question 4. Which factorizations are incorrect?

Question 3. Simplify where is the imaginary unit

Question 2. Find algebraically the zeros for by factoring

1


Practice important Algebra II concepts with these advanced problems. Insome cases, you will need to apply multiple math concepts to determine thebest or most appropriate solution format. Full solutions are at the end for

your reference. Good luck!

Question 1. What is the slope of the graph of the

equation −2x+ y =3

2?

Question 2. Find algebraically the zeros forp(x) = x3 + 2x2 − 4x− 8 by factoring

Question 3. Simplify xi(i − 7i)2 where i is theimaginary unit


A. 4x2 − 49 = (2x+ 7)(2x− 7)

B. m3 − 8y3 = (m− 2y)(m2 + 2my + 4y2)

C. a3 + 3a2 − 4a+ 12 = (a− 2)2(a+ 3)

D. k3 + 5k2 + 6k + k2 + 5k + 6 = (k + 1)(k + 2)(k + 3)

1






2?

Question 2. Find algebraically the zeros for

p(x) = x3 + 2x2 − 4x− 8 by factoring



A. 4x2 − 49 = (2x+ 7)(2x− 7)

B. m3 − 8y3 = (m− 2y)(m2 + 2my + 4y2)

C. a3 + 3a2 − 4a+ 12 = (a− 2)2(a+ 3)

D. k3 + 5k2 + 6k + k2 + 5k + 6 = (k + 1)(k + 2)(k + 3)

1






2?




A. 4x2 − 49 = (2x+ 7)(2x− 7)

B. m3 − 8y3 = (m− 2y)(m2 + 2my + 4y2)

C. a3 + 3a2 − 4a+ 12 = (a− 2)2(a+ 3)

D. k3 + 5k2 + 6k + k2 + 5k + 6 = (k + 1)(k + 2)(k + 3)

1






2?




A. 4x2 − 49 = (2x+ 7)(2x− 7)

B. m3 − 8y3 = (m− 2y)(m2 + 2my + 4y2)

C. a3 + 3a2 − 4a+ 12 = (a− 2)2(a+ 3)

D. k3 + 5k2 + 6k + k2 + 5k + 6 = (k + 1)(k + 2)(k + 3)

1






2?




A. 4x2 − 49 = (2x+ 7)(2x− 7)

B. m3 − 8y3 = (m− 2y)(m2 + 2my + 4y2)

C. a3 + 3a2 − 4a+ 12 = (a− 2)2(a+ 3)

D. k3 + 5k2 + 6k + k2 + 5k + 6 = (k + 1)(k + 2)(k + 3)

1

2

Question 5. What is the solution to

Question 6. Over the set of integers, factor this expression completely:

Question 7. Graph

?Question 5. What is the solution to8(2x+3)− 48 = 0?

A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3

Question 6. Over the set of integers, factor thisexpression completely:

4x3 − x2 + 16x− 4

Question 7. Graph y = 2 + log2(x+ 3)− 5

Question 8. Label the axes and graph the equa-tion y = 400(.85)2x − 6

Question 9. The graph of the equation y = 3x2

has its vertex at the coordinate point (0, 0). Whatcoordinate point describes the vertex of the graphof the equation y = 3x2 − 3 ?

A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)

2

Question 5. What is the solution to8(2x+3)− 48 = 0?

A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3


4x3 − x2 + 16x− 4





A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)

2


A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3


4x3 − x2 + 16x− 4





A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)

2


A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3


4x3 − x2 + 16x− 4





A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)

2

3

Question 9. The graph of the equation has its vertex at the coordinate point . What coordinate point describes the vertex of the graph of the equation ?

Question 8. Label the axes and graph the equation


A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3


4x3 − x2 + 16x− 4





A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)

2


A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3


4x3 − x2 + 16x− 4





A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)

2


A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3


4x3 − x2 + 16x− 4





A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)

2


A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3


4x3 − x2 + 16x− 4





A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)

2


A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3


4x3 − x2 + 16x− 4





A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)

2

4

Question 10. A function of is graphed below:

Which equation best describes the graph?Question 10. A function of x is graphed below:

Which equation best describes the graph?

A. y = x2 + 5

B. y = (x+ 2)2 + 1

C. y = (x− 2)2 + 1

D. y = (x+ 2)(x− 1)

3

Question 10. A function of x is graphed below:


A. y = x2 + 5

B. y = (x+ 2)2 + 1

C. y = (x− 2)2 + 1

D. y = (x+ 2)(x− 1)

3

5

SOLUTIONS

Question 1: 2

Solving with Photomath

Option 1:

• Scan the equation in Photomath to graph it

• Use the root and vertical intercept as two random points A(x1, y1)and B(x2, y2)

• Plug in A and B into the formula for slope =y2 − y1x2 − x1

Option 2:

• Scan the equation in Photomath

• Click on the Show other methods button and select the methodto Solve the equation for y

• The equation will be shown in slope-intercept form so read outthe coefficient of the x term which represents the slope of theequation

4

SOLUTIONS

Question 1: 2


Option 1:




Option 2:




4

SOLUTIONS

Question 1: 2


Option 1:




Option 2:




4

SOLUTIONS

Question 1: 2


Option 1:




Option 2:




4

SOLUTIONS

Question 1: 2


Option 1:




Option 2:




4

Question 1: 2

Solutions


Option 1:


• Use the root and vertical intercept as two random points

• Plug in and into the formula for

and

6

Option 2:


• Click on the Show other methods button and select the method to Solve the equation for y

• The equation will be shown in slope-intercept form so read out the coefficient of the term which represents the slope of the equationQuestion 10. A function of x is graphed below:


A. y = x2 + 5

B. y = (x+ 2)2 + 1

C. y = (x− 2)2 + 1

D. y = (x+ 2)(x− 1)

3

7

Question 2:−2, 2

• Scan the right side of the polynomial to factorize the expressioninto into (x+ 2)2(x− 2)

• When a function is written in the factored form, like (xp)(xq), pand q are zeros of the function. Therefore, are −2 and 2 zerosof the polynomial p(x) = (x+ 2)2(x− 2)

• Also, the first zero −2 has a multiplicity of 2 because the factoris squared

• The key here is to understand for the factored form, the zeros are−2 and 2. The first zero has a multiplicity of 2 because thefactor is squared

Question 3: −36xi

Question 4: C


• Scan the left side of each equation and then compare the factor-ization on the right

• When you scan the left side of equation C it results in a graph.Review the final solution and compare it to the left side of theoriginal equation. You’ll see the expressions are not the sameso factorization C is incorrect

Question 5: C

Question 6: (4x− 1)(x2 + 4)

Question 7:

• Scan problem to check your answer with Photomath

Question 8:


5

Question 2:−2, 2





Question 3: −36xi

Question 4: C




Question 5: C

Question 6: (4x− 1)(x2 + 4)

Question 7:


Question 8:


5

Question 2: -2, 2

Question 3:


• Scan the right side of the polynomial to factorize the expression into

• Therefore, -2 and 2 are the zeros of the polynomial

of 2 because the factor is squared. Note that the first zero -2 has a multiplicity

• When a function is written in the factored form, like ,

• The most simplied expression is

p and q are zeros of the function

Question 2:−2, 2

• Scan the right side of the polynomial to factorize the expressioninto (x+ 2)2(x− 2)

• When a function is written in the factored form, like (x−p)(x−q),p and q are zeros of the function

• Therefore, are −2 and 2 zeros of the polynomial p(x) = (x +2)2(x − 2) Note that the first zero −2 has a multiplicity of 2because the factor is squared

• The most simplified expression is (x+ 2)(x+ 2)(x− 2)

Question 3: −36xi

Question 4: C




Question 5: C

Question 6: (4x− 1)(x2 + 4)

Question 7:


Question 8:


5

Question 2:−2, 2





Question 3: −36xi

Question 4: C




Question 5: C

Question 6: (4x− 1)(x2 + 4)

Question 7:


Question 8:


5

Question 2:−2, 2





Question 3: −36xi

Question 4: C




Question 5: C

Question 6: (4x− 1)(x2 + 4)

Question 7:


Question 8:


5

Question 2:−2, 2





Question 3: −36xi

Question 4: C




Question 5: C

Question 6: (4x− 1)(x2 + 4)

Question 7:


Question 8:


5

Question 6:

Question 2:−2, 2





Question 3: −36xi

Question 4: C




Question 5: C

Question 6: (4x− 1)(x2 + 4)

Question 7:


Question 8:


5

Question 4: C

Question 5: C


• Scan the left side of each equation and then compare the factorization on the right

• For equation C, when you scan the left side, it results in a graph. Review the final solution and compare it to the left side of the original equation. You’ll see the expressions are not the same, so factorization C is incorrect

8

Question 7:

Question 9: D

Question 8:

Question 10: B



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get ready for algebra ii - photomath · tion y = 400(.85)2x −6 question 9. the graph of the...

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