Complete the square to rewrite y = x2 + 8x+ 3 in vertex form, and then identify the minimum y-value of the function.

Please answer ASAP!!!

Work Shown:

y = x^2 + 8x + 3 is the same as y = 1x^2 + 8x + 3

It is in the form y = ax^2 + bx + c

a = 1

b = 8

c = 3

Plug the values of a and b into the formula below to get the x coordinate of the vertex (h,k)

h = -b/(2a)

h = -8/(2*1)

h = -8/2

h = -4

Plug this into the original equation to get its paired y value. This will get us the value of k

y = x^2 + 8x + 3

y = (-4)^2 + 8(-4) + 3

y = 16 - 32 + 3

y = -13

This is the smallest y output possible. Therefore it is the minimum. The minimum occurs at the vertex (h,k) = (-4, -13)

We know we are dealing with a minimum because a = 1 is positive forming a parabola that opens upward. If a < 0, then the parabola would open downward to yield a maximum.

4a. is 3 miles every hour

4b. is 1/3 of an hour per mile

step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .