Question

You throw a ball straight up from a rooftop. The ball misses the rooftop and eventually strikes the ground A mathematical model can be used to describe the relationship for the ball's height above the ground, y. after x seconds. x, seconds after the ball is y, ball's height, in feet, above the ground 289 271 214 on its way down thrown 3 4 2 a. Find the quadratic function y= - ax +bx + c whose graph passes through the given points. You throw a ball straight up from a rooftop. The ball misses the rooftop on its way down and eventually strikes the ground A mathematical model can be used to describe the relationship for the ball's height above the ground, y, after x seconds. X, seconds after the ball is y, ball's height, in feet, above the thrown ground 289 1 271 214 Find the quadratic function y= ax + bx + c whose graph passes through the given points. a.

Answer 1

(a) Given: y ax2 +bx+c Require to find the quadratic functi on whose graph passes through the given point points x 1 289 a+b+c 289 x 3y 271 .(2) 9a+3c 271 x 4y214 ..(3) (a) (b) and (c) 16a +4b c= 214 Solve the equati ons (2)-(1) 8a2b =-18 4a +b-9 ...(4) (3)-(2)7ab=-57 And (5)-(4)7a+b-4a-b-57+9 (5) 3a =-48 a-16 Now a 16 b=-9-4(-16)(using (4)) b55 55-16+55 + c (using (1)) And a -16,b 289 c 289-55+16 c 250 Thereofre, y-16x2 +55x+250