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# 9.9: Chapter Test

Difficulty Level: At Grade Created by: CK-12

Multiple Choice – Please circle the letter of the correct answer and write that letter in the space provided to the left of each question.

1. _____ What is the general form of the following quadratic equation? \begin{align*}\frac{1}{2}(y-1)=(x+3)^2\end{align*}
1. \begin{align*}2x^2+6x+10\end{align*}
2. \begin{align*}2x^2+12x+17\end{align*}
3. \begin{align*}2x^2+12x+19\end{align*}
4. \begin{align*}2x^2+6x+17\end{align*}
2. _____ What are the zeros of the following quadratic equation? \begin{align*}(m+2)^2=25\end{align*}
1. \begin{align*}m=7\end{align*}; \begin{align*}m=-3\end{align*}
2. \begin{align*}m=-7\end{align*}; \begin{align*}m=3\end{align*}
3. \begin{align*}m=7\end{align*}; \begin{align*}m=3\end{align*}
4. \begin{align*}m=-7\end{align*}; \begin{align*}m=-3\end{align*}
3. _____ \begin{align*}\boxed{h(t)=-2(t-3)^2+21}\end{align*} This quadratic function represents height \begin{align*}(h)\end{align*} in yards, reached by a ball thrown into the air after \begin{align*}t\end{align*} seconds. From what height was the ball thrown?
1. 2yd
2. 5yd
3. 21yd
4. 3yd
4. _____ What is the value of the discriminant for the following quadratic equation? \begin{align*}3y^2-5y=1\end{align*}
1. \begin{align*}\sqrt{13}\end{align*}
2. \begin{align*}\sqrt{37}\end{align*}
3. 37
4. 13
5. _____ Simplify the following and express the result as a complex number. \begin{align*}(4-5i)(3+2i)\end{align*}
1. \begin{align*}22-7i\end{align*}
2. \begin{align*}2-7i\end{align*}
3. \begin{align*}-22+7i\end{align*}
4. \begin{align*}22-7 \sqrt{i}\end{align*}
6. _____ For what values of ‘\begin{align*}m\end{align*}’ does the following equation have imaginary roots? \begin{align*}4x^2+mx+9=0\end{align*}
1. \begin{align*}m=12\end{align*}; \begin{align*}m=-12\end{align*}
2. \begin{align*}m>12\end{align*}; \begin{align*}m<-12\end{align*}
3. \begin{align*}m<12\end{align*}; \begin{align*}m<-12\end{align*}
4. \begin{align*}m<12\end{align*}; \begin{align*}m>-12\end{align*}
7. _____ The length of a driveway is 5yd longer than the width. If the area of the driveway is \begin{align*}300 \ yd^2\end{align*}, what are its length and width?
1. \begin{align*}l=10 \ yd\end{align*}; \begin{align*}w=15 \ yd\end{align*}
2. \begin{align*}l=20 \ yd\end{align*}; \begin{align*}w=15 \ yd\end{align*}
3. \begin{align*}l=10 \ yd\end{align*}; \begin{align*}w=3 \ yd\end{align*}
4. \begin{align*}l=25 \ yd\end{align*}; \begin{align*}w=20 \ yd\end{align*}
8. _____ What are the exact roots of the following quadratic equation? \begin{align*}2x^2=2x+3\end{align*}
1. \begin{align*}x=\frac{1 \pm \sqrt{7}}{2}\end{align*}
2. \begin{align*}x=\frac{2 \pm \sqrt{28}}{4}\end{align*}
3. \begin{align*}x=\frac{1 \pm \sqrt{7}}{4}\end{align*}
4. \begin{align*}x=\frac{2 \pm \sqrt{-20}}{4}\end{align*}
9. _____ What is the solution for the following radical equation? \begin{align*}\sqrt{x+2}=x\end{align*}
1. the roots are 2 and 1
2. the roots are –2 and 1
3. the root is 2
4. the root is 1
10. _____ The following quadratic equation was solved using the quadratic formula. \begin{align*}x^2-4x=3\end{align*} Which step contains the first mathematical error?
11. Step 1:
12. \begin{align*}x=\frac{- \left(-4\right) \pm \sqrt{\left(-4\right)^2-4 \left(1\right) \left(-3\right)}}{2 \left(1\right)}\end{align*}
13. Step 2:
14. \begin{align*}x=\frac{4 \pm \sqrt{16-12}}{4}\end{align*}
15. Step 3:
16. \begin{align*}x=\frac{4 \pm \sqrt{4}}{2}\end{align*}
17. Step 4:
18. \begin{align*}x=3;x=1\end{align*}
1. Step 1
2. Step 2
3. Step 3
4. Step 4

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