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

 Jun 22, 2024
 #1
avatar+1075 
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First, let's combine all like terms. We get

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

 

Now, the equation for the x value of the vertex is

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

 

Thus, we have \(x=\frac{-(-6)}{2(-5)} =- \frac{6}{10}\)

 

Plugging in x into the equation for y, we have 

\(y=\frac{59}{5}\)

 

Thus the vertex is \(\left(-\frac{3}{5},\:\frac{59}{5}\right)\)

 

So our answer is \(\left(-\frac{3}{5},\:\frac{59}{5}\right)\)

 

Thanks! :)

 Jun 22, 2024

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