Q: You have 1200 ft of fencing to build a rectangular coral along a creek (so you only need to fence three sides). What are the dimensions that maximize the area?

$$300 \text{ ft} \times 600 \text{ ft}$$

Question 1

Given the quadratic function $$f(x) = -2x^2$ + 8x - 1$$, what is its vertex form?

Accepted Answer

$$f(x) = -2(x-2)^2$ + 7$$

Question 2

A fan store sells $$2000 - 25p t-$$shirts when the price is $$p$$ dollars. What price maximizes the revenue?

Accepted Answer

$$p = 20$$

Question 3

You have 1200 ft of fencing to build a rectangular coral along a creek (so you only need to fence three sides). What are the dimensions that maximize the area?

Accepted Answer

$$300 	ext{ ft} 	imes 600 	ext{ ft}$$

Question 4

A hockey arena seats 15,000. At $$\14$ per ticket, attendance is 9,500. For each $$\$$1$$ decrease, attendance increases by 1,000. What ticket price maximizes revenue?

Accepted Answer

$$\12$

Question 5

Given $$f(x) = 3x^2$ - 4x + 2$$, what is the $$x-$$coordinate of the vertex?

Accepted Answer

$$x = \frac{2}{3}$$

Question 6

Which of the following is the correct factorization of $$x^2 - 2x - 15$?

Accepted Answer

$$(x-5)(x+3)$$

Question 7

What is the factorization of $$2x^2 - 5x + 2$?

Accepted Answer

$$(2x-1)(x-2)$$

Question 8

Which of the following quadratics is a perfect square trinomial?

Accepted Answer

$$x^2 - 10x + 25$

Question 9

What is the factorization of $$x^2 - 81$?

Accepted Answer

$$(x-9)(x+9)$$

Question 10

Expand $$(x+2)(x+5)$$ and identify the values of $$b$$ and $$c in $$the standard form $$x^2 + bx + c$.

Accepted Answer

$$b = 7, c = 10$$

Question 11

Which of the following is the correct factorization of $$4x^2 + 11x - 3$?

Accepted Answer

$$(4x+3)(x-1)$$

Question 12

If a quadratic is in the form $$m^2x^2$ - n^2$, what is its factorization?

Accepted Answer

$$(mx-n)(mx+n)$$

Question 13

What is the factorization of $$9x^2 + 12x + 4$?

Accepted Answer

$$(3x+2)^2$$

Question 14

Given the quadratic $$x^2 + x - 20$, which pair of numbers multiplies to -20$ and adds to 1$?

Accepted Answer

$$5$$ and $$-4$$

Question 15

What is the factorization of $$50x^2 - 2$?

Accepted Answer

$$(5\sqrt{2}x-1)(5\sqrt{2}x+1)$$

Question 16

If the quadratic $$ax^2 + bx + c$ has a = 1$, which factoring method is typically easiest?

Accepted Answer

Sum-product method

Question 17

What is the factorization of $$100x^2 + 49$?

Accepted Answer

Cannot be factored over the real numbers

Question 18

If a quadratic trinomial factors as $$(x+a)^2$$, what must be true about its coefficients?

Accepted Answer

$$b = 2a$$ and $$c = a^2$

Question 19

If the revenue function for a product is $$R(p) = p(2000 - 25p)$$, what is the maximum possible revenue?

Accepted Answer

$$20,000$$

Question 20

If $$(y-4)(y+4) is $$expanded, what is the result?

Accepted Answer

$$y^2 - 16$

Quadratic Functions: Vertex Form, Applications, and Factoring

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