graph a quadratic function with the funcions :concave up, y-intercept = -6zeros at x= -2 and x = 3for h ( t ) = 80 t − 15 t 2 a) evaluate and interpreth (2)b) solve: h(t) =80 interpret and graph h (t)

Question

graph a quadratic function with the funcions :concave up, y-intercept = -6zeros at x= -2 and x = 3for   h  (  t  )  =  80  t  −  15      t          2      a) evaluate and interpreth (2)b) solve: h(t) =80 interpret and graph h (t)

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graph a quadratic function with the funcions :concave up, y-intercept = -6zeros at x= -2 and x = 3assume our quadratic function is   y  (  x  )  =  a      x          2        +  b  x  +  cy-intercept   =  −  6  ⇒  (  0  ,  −  6  )  ⇒  0  +  0  +  c  =  −  6  ⇒  c  =  −  6     (I)zeros at   x  =  −  2  ⇒  (  −  2  ,  0  )  ⇒  4  a  −  2  b  +  c  =  0  ⇒  4  a  −  2  b  =  −  c  ⇒  4  a  −  2  b  =  6 (II)and   x  =  3  ⇒  (  0  ,  3  )  =  9  a  +  3  b  +  c  =  0  ⇒  9  a  +  3  b  =  −  c  ⇒  9  a  +  3  b  =  6   (III)3/     4a-2b=6 (II)2/     9a+3b=6   (III)+  3  a  +  0  =  30  ⇒  a  =  1  ⇒  4  a  −  2  b  =  6  ⇒  4  −  2  b  =  6  ⇒  2  b  =  −  2  ⇒  b  =  −  1Hence   a=1,b=-1 c=-6  y  (  x  )  =      x          2        −  x  −  6or   h  (  t  )  =  80  t  −  15      t          2      a) evaluate and interpreth   (  2  )  =  80.  (  2  )  −  15.  (      2          2        )  =  160  −  60  =  100 means : h(t) passes from(2,100) point.b) solve: h(t) =80 interpret and graph h (t) =  80  t  −  15      t          2        =  80  ⇒  0  =  80  −  80  t  +  15      t          2        5  (  16  −  16  t  +  3      t          2        =  0  )  ⇒  16  −  16  t  +  3      t          2        =  0  ⇒  (  t  −  4  )  (  3  t  −  4  )  =  0

graph a quadratic function with the funcions : concave up, y-intercept = -6 zeros at x= -2 and x = 3 for h(t) = 80t - 15t^2 a) evaluate and interpreth (2) b) solve: h(t) =80 interpret and graph h (t)

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