Sandra wrote p(x) = 30x + 5x2 in vertex form. her work is below.

1. p(x) = 5x2 + 30x

2. p(x) = 5(x2 + 6x)

3. (six-halves) squared = 9;

4. p(x) = 5(x2 + 6x + 9) – 5(9)

5. p(x) = 5(x + 3)2 – 45

describe sandra’s function.

p(x) = 5(x + 3)² - 45

Step-by-step explanation:

Sandra wrote the function as p(x) = 30x + 5x².

So, this is a formula of a parabola, and this we have to convert into vertex form.

Now, rearranging the function we get

p(x) = 5(x² + 6x)

⇒ p(x) = 5(x² + 6x + 9) - 45

⇒ p(x) = 5(x + 3)² - 45

So, this is the vertex form and the vertex of the parabola is (-3,-45).

We know the formula of a parabola having vertex at (m,n) and axis parallel to positive y-axis is given by

(x - m)² = 4a(y - n)

⇒ (Answer)

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet