Question 1 (Multiple Choice Worth 1 points)

Joyce is trying to solve the equation y = x2 − 8x + 7 using the quadratic formula. She has made an error in one of the steps below. Find the step where Joyce went wrong.

Step 1: x equals negative 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end quantity, all over two times one.

Step 2: x equals negative 8 plus or minus the square root of sixty-four minus twenty-eight all over two times one.

Step 3: x equals negative 8 plus or minus the square root of thirty-six all over two times one.

Step 4: x equals negative 8 plus or minus six all over two.

Step 1

Step 2

Step 3

Step 4

Question 2 (Multiple Choice Worth 1 points)

For which value of x does the graph of y = 3x2 − 2x − 5 cross the x-axis?

negative 3 over 5

−1

−2

negative 5 over 3

Question 3 (Multiple Choice Worth 1 points)

What are the exact solutions of x2 = 4 − 7x?

x = x equals negative 7 plus or minus the square root of thirty-three all over 2

x = x equals negative 7 plus or minus the square root of sixty-five all over 2

x = x equals 7 plus or minus the square root of sixty-five all over 2

x = x equals 7 plus or minus the square root of thirty-three all over 2

Question 4 (Multiple Choice Worth 1 points)

How can you tell when a quadratic equation has no real solutions?

when the radicand is not a perfect square

Question 5 (Multiple Choice Worth 1 points)

What are the approximate solutions of 2x2 + 9x = 8 to the nearest hundredth?

x ≈ 1.22 and x ≈ 3.28

x ≈ −0.76 and x ≈ 5.26

x ≈ −1.22 and x ≈ −3.28

x ≈ −5.26 and x ≈ 0.76

Question 6 (Fill-In-The-Blank Worth 5 points)

Decide which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring.

−b b2 − 4ac 2a

Use the part of the quadratic formula that you chose above and find its value given the following quadratic equation:

2x2 + 7x + 3 = 0

Relevance
• Joyce is trying to solve the equation y = x2 − 8x + 7 using the quadratic formula. She has made an error in one of the steps below. Find the step where Joyce went wrong.

FIRST OF ALL, Y MUST EQUAL 0

Step 1: x equals negative 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end quantity, all over two times one.

THIS IS WRONG. IT SHOULD BE

POSITIVE 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end quantity, all over two times one.

Step 2: x equals POSITIVE 8 plus or minus the square root of sixty-four minus twenty-eight all over two times one.

Step 3: x equals POSITIVE 8 plus or minus the square root of thirty-six all over two times one.

Step 4: x equals POSITIVE 8 plus or minus six all over two.

Step 5 X=(8±6)/2

Step 6 X=14/2 =7

or

Step 7 X=2/2 =1