Question

f(x) = (x+2)^2+4 . what are the coordinates of the vertex?

Answer 1

Answer:

$(-2,\, 4)$.

Step-by-step explanation:

To find the vertex of this parabola, start by rewriting it in the vertex form $f(x) = a\, (x - h)^2 + k$.

Start with the original expression:

$f(x) = (x + 2)^2 + 4$.

Note that in the vertex form, the sign in front of $h$ should be a minus. However, in $f(x) = (x + 2)^2 + 4$, the sign in front of $2$ is a plus. Since adding

$f(x) = (x - (-2))^2 + 4$.

Therefore:

• $h = -2$,
• $k = 4$.

Hence, $(-2,\, 4)$ is the vertex of this parabola.