Answer:
Vertex form: y = (x+4)^2 - 9
Minimum y-value of function: [-9, ∞)
Explanation:
Vertex form: y = a(x-h)^2 + k
To convert standard form into vertex form, you will need to complete the square. To find the minimum y-value, you will need to find the vertex and see the y-value (as it is a parabola and nothing goes above/below it).
Step 1: Move 7 over to the other side (or subtract 7)
y - 7 = x^2 + 8x
Step 2: Complete the Square
y - 7 + 16 = x^2 + 8x + 16
Step 3: Factor and combine like terms
y + 9 = (x + 4)^2
Step 4: Move 9 back to the right (or subtract 9)
y = (x + 4)^2 - 9
Final Answer: y = (x + 4)^2 - 9
Your vertex is located at (h, k), so at (-4, 9). Since the highest degree coefficient is positive, the parabola is facing up. Nothing will go below the y-value of 9.