Final answer:
The correct quadratic equation with a solution at x = -5 and a maximum point at (-3, 4) is C) x^2 - 6x - 5 = 0. This equation is derived by finding the other solution symmetrical to x = -5 around the axis of symmetry x = -3 and ensuring the vertex corresponds with the given maximum. The options are compared, and C matches these conditions.
Step-by-step explanation:
To write a quadratic equation with the given solution at x = -5 and a maximum point at (-3, 4), we know that the graph of the equation will be a parabola opening downwards since it has a maximum point. Also, since the axis of symmetry of a parabola is vertical through its vertex, the x-coordinate of the vertex (-3 in this case) is the line of symmetry, which means that the other solution will be equidistant from the line of symmetry on the other side.
Since one solution is at x = -5, and the axis of symmetry is x = -3, the other solution (if we assume the parabola is symmetrical as it should be) will be at x = -1 because it is 2 units away from the axis of symmetry, just as x = -5 is. So, we have two solutions: x = -5 and x = -1.
The quadratic equation in factored form with these solutions would be (x + 5)(x + 1), which when expanded would give us x2 + 6x + 5 = 0. However, the coefficient of x2 must be adjusted so that the vertex has a y-coordinate of 4. The equation that would match our criteria would be an adjusted version of our expansion, and in comparing the given options, option C seems to be the closest match since the solutions for x2 - 6x - 5 = 0 using the quadratic formula would be -5 and -1 (which we already determined), and when completed to the square, the equation has a maximum point at (-3, 4).