Algebra 2 Unit Test #3

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Part 1: Calculator Allowed

 1 The length L (in feet) of runway needed for a small airplane to land is given by $L=0.1{x}^{2}-3x+22$ where x is the airplane’s speed (in feet per second). If a pilot is landing a small airplane on a runway 2000 feet long, what is the maximum speed at which the pilot can land? (4)

The maximum landing speed is 59.7772 feet per second.

 2 Solve the system of equations: $\left\{\begin{array}{c}-{x}^{2}-4x+1\\ x+5\end{array}\right\$ (5)

The solutions are $\left(-4,1\right)$ and $\left(-1,4\right)$.

 3 Convert to standard form: $y=2{\left(x+3\right)}^{2}+4$ (5)

$2{\left(x+3\right)}^{2}+4=2\left({x}^{2}+6x+9\right)+4=2{x}^{2}+12x+18+4=2{x}^{2}+12x+22$

 4 Convert to standard form: $y=\left(x+3\right)\left(x-4\right)$ (5)

$\left(x+3\right)\left(x-4\right)={x}^{2}+3x-4x-12={x}^{2}-x-12$

 Algebra 2 Unit Test #3

Part 2: No Calculator Allowed

For questions 5 and 6, let $f\left(x\right)={x}^{2}-2x-1$.

 5 Identify the domain, range, and y-intercept of $f\left(x\right)$. (6)

Domain: $x\in ℝ$

Range: $y\in \left[-2,\infty \right)$

y-intercept: $\left(0,-1\right)$

 6 Sketch the graph of $f\left(x\right)$. (5)

For questions 7 and 8, let $f\left(x\right)=\left(x+2\right)\left(x-2\right)$.

 7 Identify the domain, range, and all axis intercepts of $f\left(x\right)$. (7)

Domain: $x\in ℝ$

Range: $y\in \left[-4,\infty \right)$

x-intercepts: $\left(-2,0\right)$ and $\left(2,0\right)$

y-intercept: $\left(0,-4\right)$

 8 Sketch the graph of $f\left(x\right)$. (5)

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