# How do you find the axis of symmetry, and the maximum or minimum value of the function # f(x) = -2x^2-2x -1 #?

##### 2 Answers

#### Explanation:

#"given the equation of a parabola in "color(blue)"standard form"#

#•color(white)(x)f(x)=ax^2+bx+c color(white)(x);a!=0#

#• " if "a>0" then parabola has a minimum value "uuu#

#• " if "a<0" then parabola has a maximum value "nnn#

#"here "a=-2<0" hence f(x) has a maximum"#

#"the maximum/minimum occurs at the vertex "#

#"the x-coordinate of the vertex which is also the axis"#

#"of symmetry is"#

#•color(white)(x)x_(color(red)"vertex ")=-b/(2a)#

#"here "a=-2" and "b=-2#

#rArrx_(color(red)"vertex ")=-(-2)/(-4)=-1/2#

#"substitute this value into f(x) for y-coordinate"#

#rArry_(color(red)"vertex")=-2(-1/2)^2-2(-1/2)-1=-1/2#

#"equation of axis of symmetry is "x=-1/2#

#"maximum value "=-1/2#

graph{(y+2x^2+2x+1)(y-1000x-500)=0 [-10, 10, -5, 5]}

**Axis of symmetry is** **maximum value is**

**and minimum value is**

#### Explanation:

This is a quadratic equanion of form

equation of parabola. Since

opens downward and minimum point is at

Discriminant :

maximum point. Maximum vale is

Axis of symmetry is

graph{-2x^2-2x-1 [-10, 10, -5, 5]} [Ans]