Algebra 2 CP - Unit Test #03

Algebra 2

Unit Test #3

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Part 1: Calculator Allowed

The length L (in feet) of runway needed for a small airplane to land is given by $L = 0.1 x^{2} - 3 x + 22$ 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?

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The maximum landing speed is 59.7772 feet per second.

Solve the system of equations: $\{\begin{matrix} - x^{2} - 4 x + 1 \\ x + 5 \end{matrix}$

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

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

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

Convert to standard form: $y = (x + 3) (x - 4)$

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

Algebra 2

Unit Test #3

Part 2: No Calculator Allowed

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

Identify the domain, range, and y-intercept of $f (x)$ .

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Domain: $x \in ℝ$

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

y-intercept: $(0, - 1)$

Sketch the graph of $f (x)$ .

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

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

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Domain: $x \in ℝ$

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

x-intercepts: $(- 2, 0)$ and $(2, 0)$

y-intercept: $(0, - 4)$

Sketch the graph of $f (x)$ .

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