What is the vertex of # y= (x+8)^2-2x-6#?

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Answer 1 · 2017-08-18T16:50:54

See the solution below

#y = x^2 + 16x + 64 -2x -6#
#y = x^2 + 14x + 58#

Since the equation is quadratic, Its graph would be a parabola.
graph{x^2 + 14x + 58 [-42.17, 37.83, -15.52, 24.48]}

As you can see from the graph that the roots are complex for this quadratic equation.

The vertex can be found out by the following formula,
#(x,y) = (-b/(2a) , -D/(4a))#

where,
#D =# discriminant

Also
#D = b^2 - 4ac#

here,
#b = 14#
#c = 58#
#a = 1#

Plugging in the values

#D = 196 - 4(58)(1)#
#D = 196 - 232#
#D = -36#

Therefore the vertex is given by
#(x,y) = (-14/(2) , 36/4)#
#(x,y) = (-7 , 9)#