Complete the square to rewrite y = x2 + 8x + 7 in vertex form, and then identify the minimum y-value of the function.

Vertex form: y = (x+4)^2 - 9

Minimum y-value of function: [-9, ∞)

Step-by-step 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 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.

168

step-by-step explanation:

first off, we know that he drove 3.5 hours at a rate of 48 mph.

knowing that, we want to see how many miles he drove all-together.

in this case, we can just multiply 48 by 3.5.

48 * 3.5 = 168

5.762159

step-by-step explanation:

it would be 9 because when it is the nine is over five so that would mean it rounds up to 90 or 9