Question

Complete the square to rewrite y = x2 + 8x + 7 in vertex form, and then identify

the minimum y-value of the function.

Answer 1

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.