Question

For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry.

19. f(x) = __1 2 x2 + 3x + 1

20. f(x) = −__1 3 x2 − 2x + 3

Answer 1

A quedrat'c equehon ot the form fo) = ax2+bx + C %3D has maximum value when a $Is negahve a is Posih ve value wh 2) bas minimum 29 Maximum or Minimum occur at and maximum or minimum Value is fC=b) X=ニb heve axis OF Sy is 1212+3メ+1 1a) f = a ='2, b-3,(=1 a IS PoS Iive So wC WIll have a minimum Y= -3 a*12 = -0al25 %3D 24 O Minimum value = feoras) 12-0.125) 3 oas) +) %3D O.813

axis of Symettny 's X = -0.125 20) fes = - 13x2 -ax+3 a is negative so we will have maximum at r= =b ఏం a= -13 b=-2, (=3 %3D = "0076923 0Y y-0.077 a*13 Q value= f(- 0071) = -13 x(O.071) f2* f0.072)+3 = 3.076923 Max imum Q %3D 3.077 %3D axis or symetry x= -0.077

if there is any error in given expression .and given expression are as follows ,then answer are given below

19) if f(x)=x²+3x+1
minimum value = -1.25

axis of symmetry is x=-1.5

20) if f(x)=-x²-2x+3

maximum value =4

axis of symmetry x=-1

If there is no error ,then use answers in image