Pretest: Solving Quadratic Equations

Select the correct answer. Consider this quadratic equation. x2 + 3 = 4x Which expression correctly sets up the quadratic formula to solve the equation?

A. -(-4)= sqrt -(4)^2 (1)(3) ------------------------- 2(1)

Type the correct answer in the box. Solve the given equation by completing the square. x2 + 8⁢x = 38 Fill in the values of a, b, and c to complete the solutions.

x= -4 +3 sqrt 6 x=-4-3 sqrt 6

Select the correct answer. Solve the following equation for x. x2 + 8x + 7 = 0

A. x = -1; x = -7

Select the correct answer. Solve the following quadratic equation.(x − 18)2 = 1

A. x = 19 and x = 17

A rocket accelerates straight up from rest with a constant acceleration of 400 m/s2. How long will it take the rocket to reach an altitude of 20,000 meters? This problem can be represented using the following equation. (1/2)⁢400⁢t2=20,000

B. 10 seconds

Select the correct answer. The formula below gives the area of a semi-circle, A, with a radius of r. A = 12⁢π⁢r2 Solve the formula for the radius.

B. r= sqrt 2A/pi (sqrt=square root)

Select the correct answer. Which of the following equations has a maximum at (9,7)?

D. y = -x^2 + 18x − 74

Drag the tiles to the boxes to form correct pairs. Match each equation to its factorized version and solution.

24x - 6x^2 = 0 -- 6x(4 - x) = 0, Solution: x = 0, x = 4 4x - x^2 = 0 -- x(4 - x) = 0, Solution: x = 0, x = 4 2x^2 + 6x = 0 -- 2x(x + 3) = 0, Solution: x = 0, x = -3 14x - 7x^2 = 0 -- 7x(2 - x) = 0, Solution: x = 0, x = 2

Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use / for the fraction bar(s). A café owner is designing a new menu and wants to include a decorative border around the outside of her food listings. Due to the cost of printing, the border should have an area of 48 square inches. The width of the border needs to be uniform around the entire menu. She has already determined that her food listings will fit within a 13-inch by 9-inch rectangular area.

4, 44, 48, no

Select the correct answer. Solve the given quadratic equation. x2 = 121

A. x=11

Select the correct answer. What are the solutions of the quadratic equation below? 4x2 − 30x + 45 = 0

C. 15+3 sqrt 5 ------------ 4

Select the correct answer. Solve for x. x2 + 4x - 21 = 0

C. 3, -7

Select the correct answer. Find the solution(s) for x in the equation below. x2 + 7⁢x = 8

C. x = 1; x = -8

Which equation could be solved using this application of the quadratic formula? x=−2±22−4⁢(1)⁢(−4)2⁢(1)

C. x^2 + 2x − 1 = 3

Select the correct answer. Which equation has the same solutions as the equation given below? x2 + 18x + 32 = 0

D. (x + 9)^2 = 49

Select the correct answer. Solve the equation by completing the square. 0 = x2 − 14x

D. x = 0, 14

Select the correct answer. Solve the following equation by completing the square. 4⁢x2 − 16⁢x + 8 = 0

D. x=2+ sqrt 2 or x=2 - sqrt 2

Select the correct answer. What are the solutions of this quadratic equation? x2 + 4 = 8x + 5

D. x=4 = sqrt 17

Select the correct answer. A civil engineer is designing a public parking lot for the new town hall. The number of cars in each row should be six less than the number of rows in the lot. The mayor has requested that the new lot should hold twice as many cars as the current parking lot, which has space for 56 cars. Determine which equation the civil engineer can use to find the number of rows, x, he should include in the new parking lot.

D. x^2 − 6x = 112