# Math

1. Graph the quadratic equation y = x2 + x – 2. Identify the axis of symmetry and the vertex.

2. A ball is thrown from the top of a 50-ft building with an upward velocity of 24 ft/s. When will it reach its maximum height? How far above the ground will it be?

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1. 1. http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E2+%2B+x+%E2%80%93+2

2. Use your favourite method to find the vertex of the parabola,
the x-coordinate tells you the "when", the y-coordinate tells you "how high"

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2. 1. axis of symmetry ... x = -b / 2a = -1 / 2

vertex is on the axis of symmetry ... y = (-1/2)^2 - 1/2 - 2 = -5/4
vertex is ... (-1/2 , -5/4)

2. h = -16 t^2 + 24 t + 50 ... max height is at the vertex (see #1)

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3. y = x^2 + x – 2
is y big if x big or big negative-->opens up, holds water
arrange to complete square
x^2 + x = y+2
x^2 + 1 x + (1/2)^2 = y + 2 + 1/4
(x + 1/2)^2 = y + 9/4
vertex at x = -1/2 and y = -9/4
axis of symmetry is x = -1/2
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most of us do physics in meters and stuff but anyway
in your units g = 32 ft/s^2
Hi = 50 ft
Vi = 24 ft/s
v = Vi - 32 t
v = 0 at top
32 t = 24
t = 3/4 = .75 seconds to top
h = Hi + Vi t - 16 t^2
h = 50 + 24 (3/4) -16 (9/16)
= 50 + 18 - 9
= 59 ft

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4. Damon is correct about the vertex

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