find the vertex of the following parabola

Question

f(x)=-2x^2-12x-23=0

Answer 1

f(x)  =  -2x^2 - 12x - 23

This is quadratic equation of the parabola y = ax^2 + bx + c 

Comapare above two equations

a = -2, b = -12 and c = -23

x-value of the vertex

x = ( - b / 2a) 

x = ( 12 / 2 (-2) ) 

x =  12 / (-4) 

x = -3

y - value of the vertex :

y  =  c - b^2/4a

y  =  -23 - [ (-12)^2 / 4 X (-2)] 

y  =  -23 - [ 144 / (-8)] 

y  =  -23 - [ -18] 

y  =  - 23 + 18

y  =  - 5 

 

Hence, Vertex is (x, y)  =  (-3, -5)

 

Answer :

 

Vertex is (x, y)  =  (-3, -5)