Algebra 2 Unit Test #3

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Part 1: Calculator Allowed

 1 In firefighting, a good water stream can be modeled by $y=-0.003{x}^{2}+0.62x+3$, where x is the water’s horizontal distance traveled (in feet) and y is its corresponding height (in feet). If a firefighter is aiming a good water stream at a building’s window 25 feet above the ground, at what two distances can the firefighter stand from the building? (4) 45.5022 feet and 161.1645 feet.

 2 Solve the system of equations: $\left\{\begin{array}{c}{x}^{2}-4x+3\\ -x+7\end{array}\right\$ (5) $\left(-1,8\right)$ and $\left(4,3\right)$

 3 Convert to standard form: $y=2{\left(x+4\right)}^{2}-1$ (5)

$2\left({x}^{2}+8x+16\right)-1=2{x}^{2}+16x+32-1=2{x}^{2}+16x+31$

 4 Convert to standard form: $y=\left(x+6\right)\left(x+2\right)$ (5)

${x}^{2}+6x+2x+12={x}^{2}+8x+12$

 Algebra 2 Unit Test #3

Part 2: No Calculator Allowed

For questions 5 and 6, let $f\left(x\right)={x}^{2}+4x+2$.

 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: $\left(0,2\right)$

 6 Sketch the graph of $f\left(x\right)$. (5) For questions 7 and 8, let $f\left(x\right)=\left(x-4\right)\left(x-2\right)$.

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

Domain: $x\in ℝ$

Range: $y\in \left[-1,\infty \right)$

x-intercepts: $\left(2,0\right)$ and $\left(4,0\right)$

y-intercept: $\left(0,8\right)$

 8 Sketch the graph of $f\left(x\right)$. (5) Page last updated 13:20 2021-09-29