Final answer:
To find the values of b and c in the quadratic function y = 6x² + bx + c given the vertex (-5, -4), we can use the vertex form of the quadratic function and plug in the values of h, k, and the function. Simplify the equation and solve for b and c.
Step-by-step explanation:
To find the values of b and c, we can use the fact that the vertex of the quadratic function is given by the formula (h, k), where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.
In this case, the vertex is (-5, -4). So we have h = -5 and k = -4.
Now, the vertex form of a quadratic function is y = a(x - h)^2 + k. Plugging in the values for h, k, and the given quadratic function, we get:
y = 6x^2 + bx + c
-4 = 6(-5)^2 + b(-5) + c
Simplifying the equation, we have -4 = 150 - 5b + c.
From here, we can solve the equation to find the values of b and c.