Sanjay graphs a quadratic function that has x-intercepts of –3 and 7. Which functions could he have graphed? Check all that apply.

g(x) = x2 – 4x – 21
g(x) = (x – 3)(x + 7)
g(x) = 3x2 – 12x – 63
g(x) = –(x + 3)(x – 7)
g(x) = x2 + 4x – 21

Step-by-step explanation:

When r is an x-intercept of the function, (x -r) is a factor. The two given x-intercepts mean that two factors of the function are (x -(-3))(x -7). There may be a vertical scale factor that is not necessarily positive.

These factors multiply out to give ...

  (x +3)(x -7) = x^2 -4x -21 . . . . . . matches the first choice

When this expression is multiplied by 3, it matches the third choice:

  3(x +3)(x -7) = 3x^2 -12x -63

When the factored form is multiplied by -1, it matches the fourth choice:

  -(x +3)(x -7)

x = -2

y = 848

step-by-step explanation:

plug in the numbers

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