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10.10: Chapter 10 Test

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  1. True or false? The vertex determines the domain of the quadratic function.
  2. Suppose the leading coefficient a=-\frac{1}{3}. What can you conclude about the shape of the parabola?
  3. Find the discriminant of the equation and determine the number of real solutions: 0=-2x^2+3x-2.
  4. A ball is thrown upward from a height of four feet with an initial velocity of 45 feet/second.
    1. Using Newton’s law, write the equation to model this situation.
    2. What is the maximum height of the ball?
    3. When will the ball reach 10 feet?
    4. Will the ball ever reach 36.7 feet?
    5. When will the ball hit the ground?

In 5–9, solve the equation using any method.

  1. 2x^2=2x+40
  2. 11j^2=j+24
  3. g^2=1
  4. -11r^2-5=-178
  5. x^2+8x-65=-8
  6. What is the vertex of y=-(x-6)^2+5? Does the parabola open up or down? Is the vertex a maximum or a minimum?
  7. Graph y=(x+2)^2-3.
  8. Evaluate the discriminant of the following function. How many real solutions does the quadratic equation have? -5x^2-6x=1
  9. Suppose D=-14. What can you conclude about the solutions to the quadratic equation?
  10. Rewrite in standard form: y-7=-2(x+1)^2.
  11. Graph and determine the function's range and vertex: y=-x^2+2x-2.
  12. Graph and determine the function's range and y-intercept: y=\frac{1}{2} x^2+4x+5.
  13. The following information was taken from USA Today regarding the number of cancer deaths for various years.
Year Number of Deaths Per 100,000 men
1980 205.3
1985 212.6
1989 217.6
1993 212.1
1997 201.9

Cancer Deaths of Men (Source: USA Today)

(a) Find a linear regression line to fit this data. Use it to predict the number of male deaths caused by cancer in 1999.

(b) Find a quadratic regression line to fit this data. Use it to predict the number of male deaths caused by cancer in 1999.

(c) Find an exponential regression line to fit this data. Use it to predict the number of male deaths caused by cancer in 1999.

(d) Which seems to be the best fit for this data?

Texas Instruments Resources

In the CK-12 Texas Instruments Algebra I FlexBook® resource, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9620.

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