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For problems 1 – 8, solve for x. Express irrational answers in simplified radical form:
- 3(x – 4)^2 – 54 = 0 2. 3(x + 7)^2 + 36 = 0
- x^2 – 7x – 1 = 0 4. 2x^2 = 3 – 4x
Solve using the appropriate u-substitution:
- (x^2 + 2x)^2 – 14(x^2 + 2x) = 15 6. x^3
2
1
- x 7 x 8 0 8. (^12 ) x 3x 10 0
Write a quadratic equation in standard form with the given solution set:
1 2 , 2 7
- { - 8 i , 8 i }
- 2 i 3 , 2 i 3
- A company’s profit (in thousands of dollars) can be approximated over the next 15 years by the function
p ( y ) 1. 6 y^2 5 y 31 , where p ( y )is the profit and (^) y is the number of years. a.) Estimate the profit 7 years from now.
b.) Estimate the years needed for the company to break even.
- The equation for the height of a ball thrown into the air is h (^ t )^16 t^2 40 t^50 , where h ( t )is the height
of the ball after (^) t seconds. a.) Estimate the time it takes for the ball to be 30 feet above the ground.
b.) Estimate the height of the ball and seconds it takes to reach its maximum height.
- The function f(x) = -0.02x^2 + x + 1 models the yearly growth of a young redwood tree, f(x), in inches, with x inches of rainfall per year. a.) How many inches of rainfall per year does it take for the tree to grow 3 inches?
b.) How many inches of rainfall per year results in maximum tree growth and what is the maximum yearly growth?
- A 20-foot supporting wire is to be attached to the top of an antenna. The wire must be anchored at a distance from the base of the antenna and that distance is 4 feet more than the height of the antenna. How high is the antenna?
- A building casts a shadow that is double the length of the building’s height. If the distance from the end of the shadow to the top of the building is 300 meters, how high is the building? Express the answer in simplified radical form. Then find a decimal approximation to the nearest tenth of a meter.
Solve each inequality, express the answer in interval notation, and graph it on a number line.
- 2x^2 + 9x + 4 0 22. x^2 – x < 12
23. (3x-1)(x+4)(3x+6) ≤ 0 24.^0
x x
x
x
