Question

A diver jumped from a diving platform. The image shows her height above the water at several different times after leaving the platform.
Part A - Find the equation of the quadratic function that describes the relationship between the diver's time and height. Round to the nearest tenth.

(Equation has to be in standard form, y = ax^2+bx+c)

Answer 1

It is given to us that we have to use the equation in the standard form as given as:

$y=ax^2+bx+c$

which is the quadratic equation of a generalized parabola.

Now, to find the answer to the Part A all that we need to do is take selected snapshots of the divers coordinates and plug them in the given equation and then solve for the parameters a,b,c which will help us complete the quadratic function. We know that the time (in seconds) is the x coordinate and the height (in ft) is the y coordinate.

We will need (any) three of the five positions of the diver given in the question because we have three unknowns a,b and c that we need to find.

Let us take the first three positions. Thus, our equation will become:

$27=a(0.25)^2+b(0.25)+c$

$29=a(0.5)^2+b(0.5)+c$ and

$29=a(1.5)^2+b(1.5)+c$

Solving the above three equations simultaneously by using a calculator, we get the values of the three parameters (rounded) to the nearest tenths to be:

$a=-6.4, y=12.8, z=24.2$

Thus, the equation of the quadratic function that describes the relationship between the diver's time and height is:

$y=-6.4x^2 +12.8x+24.2$

Answer 2

Answer:

y = -5*x^2 + 10.2*x +24.9

Step-by-step explanation:

time (s)   height (ft)

0.25       27

0.5         29

1.5          29

2            25

2.75        15

To find the quadratic equation that correlates the data you can use either a calculator or a spreadsheet software, like MS Excel. Using Excel, first you have to input data; then select it and add a scatter plot; next, select one of the dots, left click, add regression line; finally, in the new menu, choose polynomial, degree = 2. In the picture attached, the result is shown.