Question

Given the equation of the function g(x) = (x + 10)2 - 2: The function has shifted 10 units to the (right/left/up/down) and 2 units (right/left/up/down). The coordinates of the vertex of the quadratic function are ( , ). This equation, written in standard form, would be g(x) =

Answer 1

The quadratic function g(x) has shifted 10 units left and 2 units down, with the vertex coordinates being (-10, -2). Writing the function in standard form yields g(x) = x^2 + 20x + 98.

Step-by-step explanation:

The function given is g(x) = (x + 10)^2 - 2. This is a quadratic function in the form y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

By comparing it to the standard form, we can see that the function has shifted 10 units to the left and 2 units down. The minus sign before the 10 indicates the left shift, and the minus sign before the 2 indicates the downward shift. Therefore, the coordinates of the vertex of this quadratic function are (-10, -2).

To write this function in its standard form, you would simply expand the squared binomial and combine like terms:

g(x) = x^2 + 20x + 100 - 2
g(x) = x^2 + 20x + 98