Penelope determined the solutions of the quadratic function by completing the square. f(x) = 4x2 + 8x + 1
–1 = 4x2 + 8x

–1 = 4(x2 + 2x)

–1 + 1 = 4(x2 + 2x + 1)

0 = 4(x + 2)2

0 = (x + 2)2

0 = x + 2

–2 = x

What error did Penelope make in her work?

Penelope should have subtracted 1 from both sides instead of adding 1.
Penelope should have subtracted 4 from both sides instead of adding 1.
Penelope should have added 4 to both sides instead of adding 1.
Penelope should have subtracted 8 from both sides instead of adding 1.

Arestaurant chef made 1 1/2 jars of pasta sauce. each serving of pasta requires 1/2 of a jar of sauce. how many servings of pasta will the chef be able to prepare using the sauce?

Suppose we have a set of small wooden blocks showing the 26 letters of the english alphabet, one letter per block. (think of scrabble tiles.) our set includes 10 copies of each letter. we place them into a bag and draw out one block at a time. (a) if we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) now suppose we just toss our chosen blocks into a pile, and whenever we draw a letter we already have, we put it back in the bag and draw again. how many different piles of 5 blocks could result? possible? piles will contain at least one repeated letter? (c) if we draw out 5 blocks wit hout looking at them, how many different piles are (d) if we draw out 5 blocks without looking at them, how many of the possible 2. (4) consider the following formula. 12 give two different proofs, one using the factorial formulas and the other combina torial.

(2, 4) (2, 1) (6, 12) (4, -5) (-2, 4) |(2, -4) (6, -12) (-4,5) quadrilateral abcd is reflected over the x-axis. quadrilateral abcd is translated 2 units right and 1 unit down. quadrilateral abcd is dilated by a scale factor of 3. quadrilateral abcd is rotated 180° clockwise about the origin. reset next