Final answer:
To write the equation for a quadratic function with a vertex at (-1,-3) and passing through (1,5), use the vertex form of a quadratic function, f(x) = a(x - h)^2 + k, where (h,k) is the vertex. Substitute the given values to find the value of 'a' and write the equation.
Step-by-step explanation:
To write the equation for a quadratic function with a vertex at (-1,-3) and passing through (1,5), we can use the vertex form of a quadratic function, which is given by f(x) = a(x - h)^2 + k, where (h,k) is the vertex. Substituting the given vertex values, we have f(x) = a(x + 1)^2 - 3. To find the value of 'a', we can use the fact that the function passes through (1,5). Substituting these values into the equation, we get 5 = a(1 + 1)^2 - 3. Simplifying this equation gives us 8a = 8, so a = 1. Therefore, the equation for the quadratic function is f(x) = (x + 1)^2 - 3.