Question

what is the minimum of the graph described by y= (x+4)^2 -5

Answer 1

To find the minimum of the graph described by the function \( y = (x + 4)^2 - 5 \), we can analyze the equation.

This function is a quadratic function in the form of \( y = a(x - h)^2 + k \), where:
- \( (h, k) \) is the vertex of the parabola,
- \( a \) determines the direction (upward or downward) and the width of the parabola.

In your function:

- \( a = 1 \) (the coefficient of \( (x + 4)^2 \), which is positive),
- The vertex form is \( y = (x - (-4))^2 - 5 \).

From this, we can see that:
- The vertex (h, k) is at \( (-4, -5) \).

Since the parabola opens upwards (because \( a > 0 \)), the vertex is the minimum point.

Thus, the minimum value of the graph is \( y = -5 \) at \( x = -4 \).

In conclusion, the minimum value of the function is \(-5\).