+2653 Find the vertex of the graph of the equation y = -2x^2 + 8x + 15 - 3x^2 + 7x - 25
+297 Absolutely, I’ve been improving my problem-solving abilities in simplifying polynomials. Let's find the vertex of the graph of the equation: y=−2x2+8x+15−3x2+7x−25
We can find the vertex by rewriting the equation in vertex form, which is of the form y=A(x−h)2+k
where (h,k) is the vertex.
Steps to solve: 1. Combine terms: y=(−2−3)x2+(8+7)x+(15−25) y=−5x2+15x−10
2. Factor the expression: y=−5(x2−3x+2) y=−5(x−2)(x−1)
3. The equation is already in vertex form: The coefficient of the x2 term is −5, which is negative, so the parabola opens downward. The vertex is at the point where x=2 and y=−5(2−2)(2−1)=0.
Answer: The vertex of the parabola is (2,0).
