How do you find the vertex of a parabola #y=(x+5)(x+3)#?

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Answer 1 · 2015-07-19T00:29:48

The vertex is at #color(red)((-4,-1)#.

#y = (x+5)(x+3)#

#y = x^2+8x+15#

The standard form of the equation for a parabola is

#y = ax^2 + bx + c#

By comparing the two equations, we see that

#a = 1#, #b = 8#, and #c = 15#.

The #x#-coordinate of the vertex is at #x = -b/(2a) = -8/(2×1) = -8/2 = -4#.

To find the #y#-coordinate of the vertex, we insert #x = -4# into the equation.

#y = (x+5)(x+3) = (-4+5)(-4+3) = 1(-1) = -1#

The vertex is at (#-4,-1#).

Graph