Question

What is the minimum of the graph described by: y = (x + 7)^2 + 3

Answer 1

The equation given is \( y = (x + 7)^2 + 3 \). This is in the form of a quadratic function, specifically \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola.

In this case, we have:

- \( a = 1 \) (which is positive, indicating the parabola opens upwards)
- \( h = -7 \)
- \( k = 3 \)

The vertex of the parabola occurs at \( (h, k) = (-7, 3) \).

Since the parabola opens upwards, the vertex represents the minimum point on the graph.

Thus, the minimum value of \( y \) is:

\[
\text{Minimum} = k = 3
\]

Therefore, the minimum of the graph described by the equation \( y = (x + 7)^2 + 3 \) is **3**.