The function h=−16t2+26t models the height h (in feet) of the dolphin after t seconds. after how many seconds is the dolphin at a height of 5 feet? round your answers to the nearest tenth.

Answer:The dolphin is at height 5 feet after 1.40 seconds or 0.228 seconds.Step-by-step explanation:Given : The function [tex]h=-16t^2+26t[/tex]models the height h (in feet) of the dolphin after t seconds.To Find: After how many seconds is the dolphin at a height of 5 feet?Solution:Function: [tex]h=-16t^2+26t[/tex]h is the heightt is the timeNow we are supposed to find After how many seconds is the dolphin at a height of 5 feetSubstitute h = 5So, [tex]5=-16t^2+26t[/tex][tex]16t^2-26t+5=0[/tex][tex]16t^2-26t+5=0[/tex] ---1Using quadratic formula : [tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]General quadratic equation: [tex]ax^2+bx+c=0[/tex]   ---AOn Comparing equation 1 with Aa = 16b = -26c=5Substitute the values in the quadratic formula.[tex]x = \frac{-(-26)\pm\sqrt{(-26)^2-4(16)(5)}}{2(16)}[/tex][tex]x = \frac{26\pm 18.86796}{32}[/tex][tex]x = \frac{26+18.86796}{32},\frac{26-18.86796}{32}[/tex][tex]x = 1.4021,0.2228[/tex]Thus the dolphin is at height 5 feet after 1.40 seconds or 0.228 seconds.