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Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 - 3x^2 - 14x + 25.

 Jul 10, 2024
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First, let's combine all like terms on the right side of the equation. 

We get the formula

\(y=-5x^{2}-6x+10\)

 

Now, it's important to note that the x coordinate of the vertex can be written in the form

\(\frac{-b}{2a}\) for parabolas in the form of \(y=ax^2+bx+c\)

 

Thus plugging in -5 and -6, we get

\(x=6/-10 = -3/5=-0.6\)

 

Plugging this back into the equation, we fins that \(y=11.8\)

 

Thus the vertex is at \((-0.6, 11.8)\)

So our answer is \((-0.6, 11.8)\)

 

Thanks! :)

 Jul 10, 2024

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