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

1 Answer
Aug 18, 2017

See the solution below

Explanation:

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)