find the quadratic function y = a x 2 + b x + c whose graphpasses through the given points.(1,6), (-114), (2,11)

Question

find the quadratic function   y  =  a      x          2        +  b  x  +  c whose graphpasses through the given points.(1,6), (-114), (2,11)

Christina Matthews · Accepted Answer

(1,6), (-1,14), (2,11)Now you have a function   y  =  a      x          2        +  b  x  +  cyou have one equation with three unknowns, a, b, c.You also have three points that this function passes through.when x = 1, y = 6when x = -1, y = 14when x = 2, y = 11so to figure this out you set up your equations like this so you can find your unknown.equation 1:   6  =  a  (  1      )          2        +  b  (  1  )  +  c6 = a + b + cequation 2:   14  =  a  (  −  1      )          2        +  b  (  −  1  )  +  c14 = a - b + cequation 3:   11  =  a  (  2      )          2        +  b  (  2  )  +  c11 = 4a + 2b + cnow you have three equations with 3 unknowns. Now it ispossible to solve for your unknowns.lets start by subtracting equation 1 from equation 214 = a + -b + c- (6 = a + b + c)= 8 = -2b, b = -4now that we know be we can take equation 3 and subtract from itequation 2.11 = 4a + 2b + c-(14 = a - b +c)= -3 = 3a +3bplug in b-3 = 3a +(-4)3-3 = 3a -129 =3a, a = 3now we know a and we know b so we can substitute this into anyoneof the three equations to get c.equation 1 looks easy enough6 = a + b +ca =3, b = -46 = 3+(-4) + c6 - 3 + 4 = cc =7so now we plug our values into our original equation and we aredone.  y  =  a      x          2        +  b  x  +  ca = 3, b = -4,c = 7y = 3x2 - 4x + 7

Milton Anderson · Accepted Answer

y  =  a      x          2        +  b  x  +  csubstitute those points into the equation, you&#039;ll get:(1,6) : 6 = a + b + c ...........(1)(-1,14): 14= a - b + c ...........(2)(2, 11): 11=4a +2b + c .........(3)add equations (1) and (2)20 = 2a + 2c or 10 = a + c ...........(4)a = 10 - cmultiply (2) by 2 and add to equation (3)39 = 6a + 3c ............(5)13 = 2a + csubstitute a=10-c into (5)c = 7substitute c=7 into a = 10 - c, a = 3substitute into (1) 6 = a+b+c = 7+b+3, b = -4so a = 3, b = -4, c = 7. and the equation is   y  =  3      x          2        −  4  x  +  7

find the quadratic function y=ax^2 +bx +c hose graphpasses through the given points. (1,6), (-114), (2,11)

Answered question

Answer & Explanation

New Questions in Algebra I