Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 - 3x^2 - 14x + 25.
First, let's simplify the equation a bit so we get a nice quadratic equation in standard form: y=−5x2−6x+10.
There are a lot of ways to find the vertex of a parabola, but the easiest way is to use the formula x=−b/2a and then plug that x-value into the equation to solve for y.
From the formula, x=−6/10=−3/5
Now we can substitute this x value into the original equation: y=−5∗9/25+18/5+10=9/5+10=59/5
Therefore, the vertex of the equation is (−3/5,59/5). You can even see this if you use a graphing calculator.