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.