Final answer:
The quadratic function in intercept form is -1(x - (-6))(x - (-3)). In standard form, it is -1x² + 9x - 18. In vertex form, it is -1(x - 4.5)² + 20.25.
Step-by-step explanation:
The quadratic function in intercept form can be written as y = a(x - r1)(x - r2), where 'a' is the coefficient of x², and 'r1' and 'r2' are the roots of the quadratic equation. In this case, the roots are -6 and -3, and the coefficient of x² is -1. Therefore, the quadratic function in intercept form is y = -1(x - (-6))(x - (-3)).
In standard form, the quadratic function can be written as y = ax² + bx + c, where 'a', 'b', and 'c' are the coefficients. Using the given values of the roots and coefficient, the quadratic function in standard form is y = -1x² + 9x - 18.
In vertex form, the quadratic function can be written as y = a(x - h)² + k, where (h, k) is the vertex of the parabola. To find the vertex, we can use the formula h = -b / (2a) and k = f(h), where f(h) is the value of the quadratic function at h. Plugging in the values of a, b, and h, we get the vertex form as y = -1(x - 4.5)² + 20.25.