Agraph of a quadratic function is shown below. graph of y equals negative 2 times x squared plus 40 x plus 600 what is the vertex of the parabola shown? (30, 0) (800, 10) (0, 600) (10, 800)

The correct option is 4. The vertex of the parabola is (10,800).

Step-by-step explanation:

If a quadratic function is defined as

then its vertex is

The given quadratic function is

Here, a=-2, b=40 c=400.

Substitute x=10 in the given function.

The vertex of the given function is (10,800). Therefore correct option is 4.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

600,000,000,000, or 6e14

step-by-step explanation: