Question 1

Beth has 50 yards of fencing to enclose a rectangular area as shown in the image. What is the formula for the perimeter $$p as a $$function of $$x$$ and $$w$$?

Accepted Answer

$$p = 2x + 2w$$

Question 2

Given the perimeter formula $$p = 2x + 2w$$ and $$p = 50$$, express $$w in $$terms of $$x.$$

Accepted Answer

$$w = 25 - x$$

Question 3

Express the area $$A of $$the rectangle in terms of $$x$$ only, given $$w = 25 - x.$$

Accepted Answer

$$A(x) = x(25 - x)$$

Question 4

For what value of $$x is $$the area $$A(x) = x(25 - x)$$ largest?

Accepted Answer

$$x = 12.5$$

Question 5

What is the maximum area that can be enclosed with 50 yards of fencing?

Accepted Answer

$$156.25$$ square yards

Question 6

A projectile is thrown upward so that its height above the ground after $$t$$ seconds is $$h = -10t^2$ + 200t. $$After how many seconds does it reach maximum height?

Accepted Answer

$$t = 10$$

Question 7

What is the maximum height the projectile reaches, given $$h = -10t^2$ + 200t$$?

Accepted Answer

$$1000$$ meters

Question 8

Which of the following is a polynomial? State its degree and leading term: $$f(x) = -2x + 3x^4$ - 5x^2$ + 7.$$

Accepted Answer

Polynomial, degree 4, leading term $$3x^4$$

Question 9

Is $$g(x) = \frac{2}{x} + x^3$ - 1 a $$polynomial?

Accepted Answer

No, because it contains a negative exponent

Question 10

For $$f(x) = (x-1)^2$(x^2-16$$)$, what are the real zeros?

Accepted Answer

$$x = 1, 4, -4$$

Question 11

What is the multiplicity of the zero $$x = 1$$ for $$f(x) = (x-1)^2$(x^2-16$$)$?

Accepted Answer

Multiplicity 2

Question 12

Solve the inequality $$x^2 - 3x - 10$$ \geq 0$$.

Accepted Answer

$$x \leq -2 or$$ $$x \geq 5$$

Question 13

Find the axis of symmetry for $$f(x) = x^2$ + 4x.$$

Accepted Answer

$$x = -2$$

Question 14

What is the vertex of $$g(x) = -x^2$ + 8x - 9$$?

Accepted Answer

$$(4, 7)$$

Question 15

Determine whether the graph of $$h(x) = -3x^2$ - 9 is $$concave up or concave down.

Accepted Answer

Concave down

Question 16

What is the maximum number of turning points for $$f(x) = (x-1)^2$(x^2-16$$)$?

Accepted Answer

3

Question 17

Solve the inequality $$2x^2$$ \leq 8$$.

Accepted Answer

$$-2 \leq x \leq 2$$

Precalculus Review: Optimization, Quadratics, Polynomials, and Inequalities

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