For the function , what is the minimum value of .
We are given the function , and we need to find the minimum value of .
The function is in the form , where . To minimize , we first need to minimize the exponent .
The function is a quadratic function. The vertex of a parabola described by occurs at Click "Show Answer" to reveal the answer and analysis
Click "Show Answer" to reveal the answer and analysis
Access thousands of practice questions with detailed explanations on Scholardog.
'%3e%3cpath%20fill-rule='evenodd'%20clip-rule='evenodd'%20d='M1.75736%201.75736C0%203.51472%200%206.34315%200%2012C0%2017.6569%200%2020.4853%201.75736%2022.2426C3.51472%2024%206.34315%2024%2012%2024C17.6569%2024%2020.4853%2024%2022.2426%2022.2426C24%2020.4853%2024%2017.6569%2024%2012C24%206.34315%2024%203.51472%2022.2426%201.75736C20.4853%200%2017.6569%200%2012%200C6.34315%200%203.51472%200%201.75736%201.75736ZM18.1727%206H16.026L12.4879%209.8345L9.42953%206H5L10.2925%2012.5633L5.27636%2018H7.42427L11.2963%2013.8054L14.6798%2018H19L13.4829%2011.0834L18.1727%206ZM16.4622%2016.7816H15.2724L7.50688%207.15475H8.78349L16.4622%2016.7816Z'%20fill='%23535A74'/%3e%3c/g%3e%3cdefs%3e%3cclipPath%20id='clip0_774_453'%3e%3crect%20width='24'%20height='24'%20fill='white'/%3e%3c/clipPath%3e%3c/defs%3e%3c/svg%3e){kind=small}
'%3e%3crect%20id='大小'%20width='24'%20height='24'%20transform='translate(510%20188)'%20fill='%23fff'%20opacity='0'/%3e%3cpath%20id='路径_1057'%20data-name='路径%201057'%20d='M14,2a12,12,0,0,0-1.875,23.854V17.469H9.079V14h3.047V11.356c0-3.007,1.791-4.669,4.533-4.669a18.454,18.454,0,0,1,2.686.234V9.875H17.832a1.734,1.734,0,0,0-1.956,1.874V14H19.2l-.532,3.469h-2.8v8.385A12,12,0,0,0,14,2Z'%20transform='translate(507.999%20186)'%20fill='%23535a74'/%3e%3c/g%3e%3c/svg%3e){kind=small}
'%3e%3cpath%20fill-rule='evenodd'%20clip-rule='evenodd'%20d='M0%2012C0%2017.6569%200%2020.4853%201.75736%2022.2426C3.51472%2024%206.34315%2024%2012%2024C17.6569%2024%2020.4853%2024%2022.2426%2022.2426C24%2020.4853%2024%2017.6569%2024%2012C24%206.34315%2024%203.51472%2022.2426%201.75736C20.4853%200%2017.6569%200%2012%200C6.34315%200%203.51472%200%201.75736%201.75736C0%203.51472%200%206.34315%200%2012ZM4.96484%209.49609V19.043H7.93359V9.49609H4.96484ZM4.72656%206.47656C4.72656%207.42578%205.49609%208.19531%206.44922%208.19531C7.39844%208.19531%208.16797%207.42188%208.16797%206.47656C8.16797%205.52734%207.39844%204.75781%206.44922%204.75781C5.49609%204.75781%204.72656%205.52734%204.72656%206.47656ZM16.0781%2019.043H19.043V13.8047C19.043%2011.2344%2018.4883%209.25781%2015.4844%209.25781C14.043%209.25781%2013.0742%2010.0508%2012.6797%2010.8008H12.6406V9.49609H9.79688V19.043H12.7578V14.3242C12.7578%2013.0781%2012.9922%2011.8711%2014.5352%2011.8711C16.0586%2011.8711%2016.0781%2013.2969%2016.0781%2014.4023V19.043Z'%20fill='%23535A74'/%3e%3c/g%3e%3cdefs%3e%3cclipPath%20id='clip0_774_461'%3e%3crect%20width='24'%20height='24'%20fill='white'/%3e%3c/clipPath%3e%3c/defs%3e%3c/svg%3e){kind=small}
'%3e%3cpath%20fill-rule='evenodd'%20clip-rule='evenodd'%20d='M0%2012C0%206.34315%200%203.51472%201.75736%201.75736C3.51472%200%206.34315%200%2012%200C17.6569%200%2020.4853%200%2022.2426%201.75736C24%203.51472%2024%206.34315%2024%2012C24%2017.6569%2024%2020.4853%2022.2426%2022.2426C20.4853%2024%2017.6569%2024%2012%2024C6.34315%2024%203.51472%2024%201.75736%2022.2426C0%2020.4853%200%2017.6569%200%2012ZM12%205.83594C8.59688%205.83594%205.83594%208.59688%205.83594%2012C5.83594%2015.4031%208.59688%2018.1641%2012%2018.1641C15.4031%2018.1641%2018.1641%2015.4031%2018.1641%2012C18.1641%208.59688%2015.4031%205.83594%2012%205.83594ZM12%2015.9984C9.79219%2015.9984%208.00156%2014.2078%208.00156%2012C8.00156%209.79219%209.79219%208.00156%2012%208.00156C14.2078%208.00156%2015.9984%209.79219%2015.9984%2012C15.9984%2014.2078%2014.2078%2015.9984%2012%2015.9984ZM18.4078%207.0312C19.2%207.0312%2019.8469%206.38902%2019.8469%205.59214C19.8469%204.79995%2019.2%204.15308%2018.4078%204.15308C17.6156%204.15308%2016.9688%204.79526%2016.9688%205.59214C16.9688%206.38433%2017.6109%207.0312%2018.4078%207.0312Z'%20fill='%23535A74'/%3e%3c/g%3e%3cdefs%3e%3cclipPath%20id='clip0_774_455'%3e%3crect%20width='24'%20height='24'%20fill='white'/%3e%3c/clipPath%3e%3c/defs%3e%3c/svg%3e){kind=small}