David throws a ball vertically upward from a height of 3 meters. after 1 second, the ball is at a height of 12.5 meters. after 2 seconds, it’s at a height of 11.8 meters. write an equation to model the ball's height, f(x), at different times, x.

f(x) = -5.1x² +14.6x +3

Step-by-step explanation:

The three given points are obviously not on a line, but can be modeled exactly by a 2nd degree polynomial. (The degree is 1 less than the number of points.) I find it convenient to let a graphing calculator's quadratic regression function tell me the coefficients.

Solving by hand

Since the "y-intercept" is 3, the equation can be written

... f(x) = ax² +bx + 3

Filling in the given numbers, we have 2 equations in the 2 unknowns, a and b.

... f(1) = 12.5 = a·1² +b·1 +3

... f(2) = 11.8 = a·2² +b·2 +3

Simplifying these gives ...

Subtracting the first equation from the second gives ...

... (2a +b) -(a +b) = (4.4) -(9.5)

... a = -5.1

The first equation tells us

... b = 9.5 -a = 9.5 +5.1

... b = 14.6

The equation is f(x) = -5.1x² +14.6x +3.

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.