Final answer:
The vertex of the parabola y = -(x-9)² - 4 is located at (-9, -4).
Step-by-step explanation:
The equation y = -(x-9)² - 4 is in vertex form, which is given by y = a(x-h)² + k, where (h, k) is the vertex of the parabola.
In this case, the vertex is located at (-9, -4). The negative sign in front of (x-9)² indicates that the parabola opens downward.
So, the vertex of the parabola is located at (-9, -4).
The claimed vertex (-9, -4) for the quadratic equation y=-(x-9)²-4 is incorrect. The correct vertex is (9, -4) based on the equation's standard form. The quadratic formula is used to find solutions for quadratic equations and involves specific constant values.
The student's statement that the vertex of the equation y=-(x-9)²-4 is located at (-9,-4) is incorrect. The correct vertex form of a quadratic equation is y=a(x-h)²+k, where the point (h, k) is the vertex of the parabola. In this case, the equation can be rewritten as y=-1*(x-9)²-4, indicating that the vertex is actually at (9, -4).
When dealing with the quadratic formula, which is x = (-b ± sqrt(b² - 4ac))/(2a), we apply it to a quadratic equation of the form at² + bt + c = 0. For example, if we have constants a = 4.90, b = 14.3, and c = -20.0, we would substitute these into the quadratic formula to find the solutions for t.