Question

What is the minimum of the graph described by y=(x+7)2 +3
?(1 point)
Responses

(−7, 3)
(−7, 3)

(7, 3)
(7, 3)

(7, −3)
(7, −3)

(−7, −3)

Answer 1

To find the minimum of the graph described by the equation \( y = (x + 7)^2 + 3 \), we can analyze the form of the equation.

This equation is in the vertex form of a parabola \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola. Here, the terms can be identified as:

- The expression \((x + 7)^2\) indicates that the vertex occurs at \( x = -7 \).
- The \( +3 \) means that the vertex's \( y \)-coordinate is \( 3 \).

Since the coefficient of the squared term is positive (which means the parabola opens upward), the vertex is indeed the minimum point of the graph.

Thus, the minimum point is:
\[
(-7, 3)
\]

So the correct response is:
\[
\text{(−7, 3)}
\]