y = −0.009t2 + 0.274t + 0.455.

Question

Find the vertex of this parabola. (Round your answer to two decimal places.)

(t, y) = 

Answer 1

y = -.009t^2 + .274t + .455

factor out -.009 from the t and t^2 terms, then add inside the parentheses the square of half the coefficient of the t term. then add .009(.137/.009)^2 outside the brackets, so you're adding and subtracting the same number.

= -.00[(t^2 + (- .274/.009)t + (-.137/.009)^2] + .455 + (-.137^2/.009)

= -.009(t - .137/.009)^2+ .455 + 2.085444....

= - .009(t - 15.222...)^2 + 2.540444...

vertex is: (t,y) = (15.22, 2.54) = the maximum point of a downward opening parabola, which has a y intercept of 0.455