Math Homework: Vertex and Parabola

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jvyzne

Mathematics

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1. Find the vertex, and x and y intercepts of y = 4x² – 5x +5. 2. Identify the vertex and focus of the parabola y2 =-13x. 3. Solve. x(x+6)(x-6) > 0 4. Solve and graph the solution to the inequality on the real line. 1 - 5 x + 4 5. Solve log2(x + 3) - log2(x - 1) = 5 3 6. Solve equation log; (6x) () = 2 7. Determine the balance A (to the nearest cent) for P = 3,500 dollars invested at a rate r = 10% for t = 10, compounded 12 times per year. 20r 8. Solve the exponential equation 100,000 = 50,000e? for r to determine the interest rate required for an investment of $50,000 to double in value when compounded continuously for 20 years. Round your answer to one decimal place. 9. The value of a piece of property doubles every 16 years. You buy the property for $54,000. Its value t years after the date of purchase should be V(t) = 54,000(2):16. Use the model to approximate (to the nearest thousand dollars) the value of the property after 4 years. 10. Find the inverse function. f (t) = t? - 9 11. Evaluate the logarithm. 64 log 256 12. Use a calculator to evaluate lo g 30 110 by means of the change-of-base formula. Round your answer to four decimal places. 13. Identify the center and radius of the circle 16x² +16 y2 – 25 = 0. 14. Write the standard form of the equation of the parabola with focus (0,-5) and its vertex at the origin. 15. A semicircular arch for a tunnel under a river has a diameter of 80 feet (see figure). Determine the height of the arch 10 feet from the edge of the tunnel. 10ft + 14 80 ft-
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