Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 - 3x^2 - 14x + 25.
y = -2x^2 + 8x - 15 - 3x^2 - 14x + 25
Combine like terms y = –5x2 – 6x + 10
The easiest way – the easiest way I know, anyway – is
to set the first derivitive equal to zero, and solve for x.
dy/dx = –10x – 6
0 = –10x – 6
10x = –6
x = –0.6 this is the x-coordinate of the vertex
plug it back into the original equation
y = –5(–0.62) – 6(–0.6) + 10
y = –1.8 + 3.6 + 10
y = 11.8 this is the y-coordinate of the vertex
The vertex is located at (–0.6 , 11.8)
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