Answer:
The vertex of given linear equation is
x = [tex]\frac{- 7}{6}[/tex] , y = [tex]\frac{97}{12}[/tex]
Step-by-step explanation:
Given linear equation as :
y = - 3 x²- 7 x + 4
The standard equation can be written as :
y = a x² +b x + c
Now , x = ( - [tex]\frac{b}{2a}[/tex] )
So, From given equation y = - 3 x²- 7 x + 4
x = ( - [tex]\frac{b}{2a}[/tex] )
Or, x = ( - [tex]\frac{- 7}{2(-3)}[/tex] )
Or, x= ( [tex]\frac{- 7}{6}[/tex] )
Put the value of x in given equation
So , y = - 3 x²- 7 x + 4
Or, y = [tex]-3\times (\frac{-7}{6})^{2}-7\times (\frac{-7}{6})+4[/tex]
∴ y = - [tex]\frac{49}{12}[/tex] + [tex]\frac{49}{6}[/tex] + 4
Or , y = [tex]\frac{-49 +98 +48}{12}[/tex]
So , y = [tex]\frac{97}{12}[/tex]
Hence The vertex of given linear equation is x = [tex]\frac{- 7}{6}[/tex] , y = [tex]\frac{97}{12}[/tex] Answer
