Question

When f (x)= 4x^2 + 12x + 10 is rewritten in the equivalent form g(x)= 4(x+3/2)^2+1, what is the y-coordinate of the vertex represented in this function?

Answer 1

The y-coordinate of the vertex for the function g(x) = 4(x + 3/2)^2 + 1 is 1.

Step-by-step explanation:

When the quadratic function f (x) = 4x^2 + 12x + 10 is rewritten in the equivalent form g(x) = 4(x + 3/2)^2 + 1, the function is now in vertex form. The vertex form of a quadratic function is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. So by comparing, we can identify that h is -3/2, and k is 1. Therefore, the y-coordinate of the vertex represented in function g(x) is 1.