Write a quadratic equation
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1. Solve.
Let f(x) = (x - 8)^2. Find x so that f(x) = 100.
2. Write a quadratic equation having the given numbers as solutions.
7, -4
3. Complete the square by filling in the two blanks so as to produce a true equation.
x^2 + 8x + __ = (x + __)^2
x^2 + 8x + 64; (x+8)^2
x^2 + 8x + 16; (x+4)^2
x^2 + 8x; (x+4)^2
x^2 + 8x + 16; (x-4)^2
4. Solve by applying the Quadratic Formula; all radicals should be simplified as far as possible. Show your work.
x^2 + 4x + 13 = 0
5. Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
25x^2 - 10x + 1 = 0
Two different rational solutions
Two different irrational solutions
Two different imaginary solutions
Exactly one rational solution
6. Solve by applying the Quadratic Formula; all radicals should be simplified as far as possible. Show your work.
3x^2 - 2x + 3 = 0.
7. Use the quadratic formula to determine the x-intercepts (if any) of the following function. Then evaluate the function for several values of x, and use the resulting points to graph the function. Show your work.
f(x) = -x^2 - 2x - 1
8. Solve the problem.
The distance traveled by an object moving in a straight line is given by s = t2 - 8t, where s is in feet and t is the time in seconds the object has been in motion. How long (to the nearest tenth) will it take the object to move 9 feet? Show your work.
9. Translate the problem situation to a system of equations. Do not attempt to solve.
Anne has 11 coins in her pocket consisting of nickels and dimes only. The total value of the coins is $0.85. How many nickels and how many dimes does she have? (Let x represent the number of nickels and y represent the number of dimes.)
x + y = 11, 0.05x + 0.1y = 85
x + y = 11, 5x + 10y = 85
x + y = 11, 5x + 5y = 85
x + y = 11, 5x + 10y = 0.85
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Solution Summary
Quadratic Formula is applied.
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