Solving Quadratic Equations by Completing the Square: Mastery Test

Determine which equation has the same solutions as the given equation. 2x2 − 12x − 50 = 0

A:(x − 3)2 = 34

Solve the following equation by completing the square. 1/4⁢x^2 + X + 1/4 = 0

B: x = -2 + sqrt 3 or x = - 2 - sqrt 3

Select the correct answer. The equation can be solved by completing the square. What number should go in the blanks for the first step? x^2 − 18⁢x + _ = 4 + _

B:81

Determine which equation has the same solutions as the equation below. 4x2 + 32x − 28 = 0

C:(x + 4)2 = 23

Select the correct answer from each drop-down menu. Consider the given quadratic equations. Equation AEquation BEquation CEquation Dy = 3x2 − 6x + 21y = 3x2 − 6x + 18y = 3(x − 1)2 + 18y = 3(x − 1)2 + 21

Complete the following statement. Equations A and C are equivalent, and of those, equation c is in the form most useful for identifying the extreme value of the functions it defines

Type the correct answer in each box. Use numerals instead of words. Consider the quadratic equation x2 − 20x + 13 = 0.

Completing the square leads to the equivalent equation (x − 10)^2 = 87

Which statement is true about the extreme value of the given quadratic equation? y = -3x2 + 12x − 33

D:The equation has a maximum value with a y-coordinate of -21.

Solve the equation by completing the square. 0 = 4x2 − 64x + 192

D:x = 4, 12

Type the correct answer in each box. Use numerals instead of words. Consider the given quadratic equation. 4⁢x^2 + 8⁢x + 27 = 88

In order to solve by completing the square, what number should be added to both sides of the equation? 1. How many of the solutions to the equation are positive? 1. What is the approximate value of the greatest solution to the equation, rounded to the nearest hundredth? 3.03

Which of the following statements are true about the equation below? x^2 - 6x = 2 = 0

The graph of the quadratic has a minimum value The extreme value is at point (3, -7) The solutions are x = 3 + sqrt 7

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Rewrite the following equation in the form y = a(x - h)2 + k. Then, determine the x-coordinate of the minimum. y = 2x^2 - 32x + 56

The rewritten equation is y = 2 (x - 8)^2 +

Solve the equation by completing the square. x^2 + 20x + 82 = 7

The solutions, in order from least to greatest, are x = -15 and x = -5

Select the correct answer from each drop-down menu. Consider the equations below. A.y = 3⁢x^2 + 6⁢x + 18 B.y = −3⁢(x − 2)^2 + 5 C.y = 3⁢(x − 1)⁢(x + 3) D.y=−3⁢x^2 + 12⁢x

Use the equations to complete the following statements. Equation B; reveals its extreme value without needing to be altered. The extreme value of this equation has a maximum at the point (2, 5).

Complete the square for the following quadratic equation to determine its solutions and the location of its extreme value. y = −x^2 + 4⁢x + 12

x = -2,6 extreme value at (2,16)