# How do you find the axis of symmetry, and the maximum or minimum value of the function #y= -x^2-10x+7#?

##### 2 Answers

#### Explanation:

#"We require to find the vertex and determine if maximum"#

#"or minimum turning point"#

#"the equation of a parabola in "color(blue)"vertex form"# is.

#•color(white)(x)y=a(x-h)^2+k#

#"where "(h,k)" are the coordinates of the vertex and a"#

#"is a multiplier"#

#x=h" is the axis of symmetry"#

#"to obtain this form use "color(blue)"completing the square"#

#y=-(x^2+10x-7)#

#color(white)(y)=-(x^2+2(5)x+25-25-7)#

#color(white)(y)=-(x+5)^2+32#

#color(magenta)"vertex "=(-5,32)#

#"Since "a<0" then maximum turning point "nnn#

#"axis of symmetry is "x=-5#

#"and maximum value "=32#

graph{-x^2-10x+7 [-80, 80, -40, 40]}

**Axis of symmetry:**

**Maximum value**

#### Explanation:

The given equation:

The above equation is in standard form of downward parabola

**Axis of symmetry:**

**Vertex**

Maximum value of given quadratic function will be at the vertex

Hence, the maximum value of given function is obtained by setting