MAT 121 Quiz 6 Fall 2016 Section Name, Show your work for full credit. Find the

Question

MAT 121 Quiz 6 Fall 2016 Section Name, Show your work for full credit. Find the vertex, equation of the axis of sy 1)f(x) = 4x2-16x + 13 rtex, equation of the axis of symmetryof the parabola and write the equation in the vertex format. Vertex: Axis of Symmetry The equation (in vertex format): Solve. 2) A projectile is thrown upward so that its distance above the ground after t seconds is h(t) -162+630t. (a)After how many seconds does it reach its maximum height? (b) what is its maximum height? (2 pts) 6x 4-24- x-6x x2-6x Solve for x. Solve forx. 3)--6-x-22.-

Explanation / Answer

1) f(x) = 4x^2 - 16x + 13

vertex form is given by f(x) = a(x-h)^2 + k

writing the equation in vertex form

f(x) = 4( x^2 - 4x ) + 13

= 4( x- 2)^2 -16 + 13

f(x) = 4(x-2)^2 - 3

vertex = ( 2 , -3 )

axis of symmetry is the line that divides parabola into two equal halves

axis of symmtery is x = 2

2) h(t) = -16t^2 + 630 t

a)   it reaches maximum height at t = -b/2a

b = 630 , a = -16

t = -630 / 2*-16 = 19.68

after 19.68 seconds it reaches its maximum height

b) maximum height is

h(t) = -16(19.68)^2 + 630 (19.68)

maximum height = 6201.56

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