Question

quadratics & completing the square question

Answer 1

@ranga

Answer 2

A) f(t) = -16t^2 - 64t + 80
They ask you to factor the function:
f(t) = -16(t^2 + 4t - 5) = -16(t^2 + 5t - t - 5) = -16{ t(t+5) - 1(t+5) }
f(t) = -16(t+5)(t-1)
x-intercepts are when f(t) = 0. That happens when t = -5 and t = 1.
t = -5 can be ignored because t represents time and negative time is not allowed.
so when t = 1, f(t) = 0. Since f(t) measures height, at time t = 1 second, the bag hits the ground and hence height f(t) = 0.

Answer 3

B) complete the square of f(t) = -16t^2 - 64t + 80
f(t) = -16(t^2 + 4t - 5)
f(t) = -16{ (t+2)^2 - 2^2 - 5 }
f(t) = -16{ (t+2)^2 - 9 }
f(t) = -16(t+2)^2 + 144
Compare it to the standard vertex form: a(x-h)^2 + y where (h,k) is the vertex.
h = -2, k = 144. So (-2, 144) is the vertex.
Since the coefficient of x^2 is negative, this is an inverted parabola and so the vertex will be a maximum.

Answer 4

C) Since the vertex is at (-2, 144) and this is a vertical parabola the axis of symmetry will be parallel to the y-axis and pass through the vertex. Therefore, the equation for the axis of symmetry is x = -2.