find vortex, find zeros, and sketch graph, Quadratics,parabolas Y=2x^2+12x+10

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To find the vertex, you can use the formula "x = -b/2a" to find the x coordinate of the vertex, a, b, and c coming from the equation "y = ax^2 + bx + c".  So, a = 2, b = 12, c = 10.  So, for the x coordinate:

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To find the vertex, you can use the formula "x = -b/2a" to find the x coordinate of the vertex, a, b, and c coming from the equation "y = ax^2 + bx + c".  So, a = 2, b = 12, c = 10.  So, for the x coordinate:

x = -12/(2*2) = -3

So, to find the y, we plug that back into the equation:

y = 2(-3)^2 + 12(-3) + 10

   = 18 + (-36) + 10 = -8

So, the vertex = (-3,-8)

 

To find the zeros, we plug in 0 for y.  So, we solve:

0 = 2x^2 + 12x + 10

Solving that equation for x:

0 = (2x + 2)(x + 5)

2x+2 = 0   and   x+5 = 0

x = -1   and x = -5

Or, the zeros would be (-1,0) and (-5,0)

 

So, graphing the equation:

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