~asap offering 20 points and mark brainiest for correct answer~

f(x) = -1/2x^2 + 40x

Step-by-step explanation: Let the blanks be a, b, and c according to the standard f(x) = ax^2 + bx + c. To find c, plug (0, 0) into the equation: 0 = 0x^2 + 0x + c

This simplifies to 0 = c

To find b, we can pick any two x and f(x) values to be subtracted. I will use 4, 152 and 6, 222.

4, 152 plugged into the equation is 152 = 16a + 4b (Multiply 4 by itself for a)

Divide the entire equation by 4 to simplify: 38 = 4a + b

6, 222 is 222 = 36a + 6b (Multiply 6 by itself for a)

Divide the entire equation by 6 to simplify: 37 = 6a + b

We can now subtract the two equations (the b cancels out): 1 = -2a

Divide both sides by -2 to get -1/2 = a

We can now solve for b by plugging -1/2 into the equation 37 = 6a + b

37 = 6(-1/2) + b

37 = -3 + b

Add 3 on both sides: 40 = b

This means that the function that models the situation is f(x) = -1/2x^2 + 40x + 0 (the zero does not need to be included for c)

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.