What is the quadratic function f(x)=(x+3)^2+1 in standard form?

Answer 1

To express the quadratic function f(x)=(x+3)^2+1 in standard form, we need to expand the expression and simplify.

Expanding (x+3)^2, we get:
(x+3)(x+3) = x(x+3) + 3(x+3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9.

Now we can rewrite the function in standard form by combining like terms:
f(x) = (x+3)^2 + 1 = x^2 + 6x + 9 + 1 = x^2 + 6x + 10.

Therefore, the quadratic function f(x)=(x+3)^2+1 in standard form is f(x) = x^2 + 6x + 10.