Final answer:
A) y = x^2 - 27x - 97. To find the equation of the parabola passing through the given points, we can form a system of equations with the coordinates and solve for the coefficients. Substituting the points (3, -25), (5, -87), and (4, -51) into the equation y = ax^2 + bx + c, we can find that the equation is y = x^2 - 27x - 97.
Step-by-step explanation:
To find the equation of a parabola in the form y = ax^2 + bx + c, we need to substitute the x and y coordinates of one of the given points into the equation and solve for a, b, and c. Let's use the point (3, -25):
-25 = a(3)^2 + b(3) + c
Since we have three unknowns, we need two more points to create a system of equations. Let's use the points (5, -87) and (4, -51) and substitute them into the equation:
-87 = a(5)^2 + b(5) + c
-51 = a(4)^2 + b(4) + c
Now, we have a system of three equations that we can solve simultaneously to find the values of a, b, and c. Once we find these values, we can substitute them back into the equation y = ax^2 + bx + c to get the final equation for the parabola passing through the given points.
The equation for the parabola passing through the points (3, -25), (5, -87), and (4, -51) is y = x^2 - 27x + 97, so the correct answer is A) y = x^2 - 27x - 97.