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1. The graph of y = ax2 + bx + c passes through the points (1, –8), (2, –1), (3, 4), and (5, 8). If the maximum valueof y occurs at x = 5, through which other point must the graph of y pass?
2. For what values of x is the equation 2x2 = 4x + 3 true?
3. A cannonball is shot out of a cannon at a 45° angle with an approximate speed of 283m/s. The cannon from which the ball was fired sits on the edge of a cliff, and itsheight above the ground is 20 meters. The equations given above represent the cannonball'sheight above the ground (y) and its horizontal distance (x) from the face of the cliff, t seconds after it was fired, where t ≥ 0. How many seconds after the ball was fired does its vertical height above theground equal its horizontal distance from the cliff?
4. The approximate height h of an object launched vertically upward after an elapsed time t is represented by the equation, where a is acceleration due to gravity, v0 is the object's initial velocity, and h0 is the object's initial height. The table above gives the acceleration due to gravityon Earth's moon and several planets. If two identical objects are launched verticallyupward at an initial velocity of 40 m/s from the surfaces of Mars and Earth's moon,approximately how many more seconds will it take for the moon projectile to returnto the ground than the Mars projectile?
5. In the quadratic equation above, j and k are constants. What are the solutions for x?
6. If x2 – 2x – 15 = (x + r)(x + s) for all values of x, what is one possible value of r – s?
7. If k is a positive integer less than 17, what is the total number of possible integersolutions for the equation x2 + 8x + k = 0?
8. All 50 states have legislation regarding pool safety, the majority of which includesa requirement for a safety fence around the perimeter of the top of an in-ground pool.If a rectangular in-ground pool has a length that is 2 feet less than twice its width,and the area of the top of the pool is 480 square feet, how many linear feet of fencingare required, assuming the fence is placed 1 foot from the edge of the water on allsides?
9. If x – 4 is a factor of x2 – kx + 2k, where k is a constant, what is the value of k?
10. Which of the following are zeros of the quadratic equation? (Note:)
11. Which of the following is equivalent to?
12. Which of the following showswritten as a complex number in the form a + bi? (Note: i2 = -1)
13. What is the value of?
14. Which of the following is a solution to the equation? (Note:)
15. What iswritten in simplest form? (Note:)
16. If u and v are complex numbers such that u = 3 – 5i and v = -6 + i, which of the following is equivalent to (u + v)2? (Note: i2 = -1)
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