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# 10.9: Chapter 10 Review

Difficulty Level: At Grade Created by: CK-12

Define each term.

1. Vertex
2. Standard form for a quadratic equation
3. Model
4. Discriminant

Graph each function. List the vertex (round to the nearest tenth, if possible) and the range of the function.

1. \begin{align*}y=x^2-6x+11\end{align*}
2. \begin{align*}y=-4x^2+16x-19\end{align*}
3. \begin{align*}y=-x^2-2x+1\end{align*}
4. \begin{align*}y=\frac{1}{2} x^2+8x+6\end{align*}
5. \begin{align*}y=x^2+4x\end{align*}
6. \begin{align*}y=- \frac{1}{4} x^2+8x-4\end{align*}
7. \begin{align*}y=(x+4)^2+3\end{align*}
8. \begin{align*}y=-(x-3)^2-6\end{align*}
9. \begin{align*}y=(x-2)^2+2\end{align*}
10. \begin{align*}y=-(x+5)^2-1\end{align*}

Rewrite in standard form.

1. \begin{align*}x-24=-5x\end{align*}
2. \begin{align*}5+4a=a^2\end{align*}
3. \begin{align*}-6-18a^2=-528\end{align*}
4. \begin{align*}y=-(x+4)^2+2\end{align*}

Solve each equation by graphing.

1. \begin{align*}x^2-8x+87=9\end{align*}
2. \begin{align*}23x+x^2-104=4\end{align*}
3. \begin{align*}13+26x=-x^2+11x\end{align*}
4. \begin{align*}x^2-9x=119\end{align*}
5. \begin{align*}-32+6x^2-4x=0\end{align*}

Solve each equation by taking its square roots.

1. \begin{align*}x^2=225\end{align*}
2. \begin{align*}x^2-2=79\end{align*}
3. \begin{align*}x^2+100=200\end{align*}
4. \begin{align*}8x^2-2=262\end{align*}
5. \begin{align*}-6-4x^2=-65\end{align*}
6. \begin{align*}703=7x^2+3\end{align*}
7. \begin{align*}10+6x^2=184\end{align*}
8. \begin{align*}2+6x^2=152\end{align*}

Solve each equation by completing the square then taking its square roots.

1. \begin{align*}n^2-4n-3=9\end{align*}
2. \begin{align*}h^2+10h+1=3\end{align*}
3. \begin{align*}x^2+14x-22=10\end{align*}
4. \begin{align*}t^2-10t=-9\end{align*}

Determine the maximum/minimum point by completing the square.

1. \begin{align*}x^2-20x+28=-8\end{align*}
2. \begin{align*}a^2+2-63=-5\end{align*}
3. \begin{align*}x^2+6x-33=4\end{align*}

Solve each equation by using the Quadratic Formula.

1. \begin{align*}4x^2-3x=45\end{align*}
2. \begin{align*}-5x+11x^2=15\end{align*}
3. \begin{align*}-3r=12r^2-3\end{align*}
4. \begin{align*}2m^2+10m=8\end{align*}
5. \begin{align*}7c^2+14c-28=-7\end{align*}
6. \begin{align*}3w^2-15=-3w\end{align*}

In 45-50, for each quadratic equation, determine:

(a) the discriminant

(b) the number of real solutions

(c) whether the real solutions are rational or irrational

1. \begin{align*}4x^2-4x+1=0\end{align*}
2. \begin{align*}2x^2-x-3=0\end{align*}
3. \begin{align*}-2x^2-x-1=-2\end{align*}
4. \begin{align*}4x^2-8x+4=0\end{align*}
5. \begin{align*}-5x^2+10x-5=0\end{align*}
6. \begin{align*}4x^2+3x+6=0\end{align*}
7. Explain the difference between \begin{align*}y=x^2+ 4\end{align*} and \begin{align*}y=-x^2+4\end{align*}.
8. Jorian wants to enclose his garden with fencing on all four sides. He has 225 feet of fencing. What dimensions would give him the largest area?
9. A ball is dropped off a cliff 70 meters high.
1. Using Newton’s equation, model this situation.
2. What is the leading coefficient? What does this value tell you about the shape of the parabola?
3. What is the maximum height of the ball?
4. Where is the ball after 0.65 seconds?
5. When will the ball reach the ground?
10. The following table shows the number of hours spent per person playing video games for various years in the United States. \begin{align*}& x && 1995 && 1996 && 1997 && 1998 && 1999 && 2000\\ & y && 24 && 25 && 37 && 43 && 61 && 70\end{align*}
1. What seems to be the best function for this data?
2. Find the best fit function.
3. Using your equation, predict the number of hours someone will spend playing video games in 2012.
4. Does this value seem possible? Explain your thoughts.
11. The table shows the amount of money spent (in billions of dollars) in the U.S. on books for various years. \begin{align*}& x && 1990 && 1991 && 1992 && 1993 && 1994 && 1995 && 1996 && 1997 && 1998\\ & y && 16.5 && 16.9 && 17.7 && 18.8 && 20.8 && 23.1 && 24.9 && 26.3 && 28.2\end{align*}
1. Find a linear model for this data. Use it to predict the dollar amount spent in 2008.
2. Find a quadratic model for this data. Use it to predict the dollar amount spent in 2008.
3. Which model seems more accurate? Use the best model to predict the dollar amount spent in 2012.
4. What could happen to change this value?
12. The data below shows the number of U.S. hospitals for various years. \begin{align*}& x && 1960 && 1965 && 1970 && 1980 && 1985 && 1990 && 1995 && 2000\\ & y && 6876 && 7123 && 7123 && 6965 && 6872 && 6649 && 6291 && 5810\end{align*}
1. Find a quadratic regression line to fit this data.
2. Use the model to determine the maximum number of hospitals.
4. In what years were there approximately 7,000 hospitals?
5. What seems to be the trend with this data?
13. A pendulum’s distance is measured and recorded in the following table. \begin{align*}& swing && 1 && 2 && 3 && 4 && 5 && 6\\ & length && 25 && 16.25 && 10.563 && 6.866 && 4.463 && 2.901\end{align*}
1. What seems to be the best model for this data?
2. Find a quadratic regression line to fit this data. Approximate the length of the seventh swing.
3. Find an exponential regression line to fit this data. Approximate the length of the seventh swing.

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