Question

The table shows the approximate height of a projectile x seconds after being fired into the air. Which equation models the height, y, x seconds after firing? y = –10(x)(x – 5) y = 10(x)(x – 5) y = –10(x – 5) y = 10(x – 5)The table shows the approximate height of a projectile x seconds after being fired into the air.


Which equation models the height, y, x seconds after firing?

y = –10(x)(x – 5)
y = 10(x)(x – 5)
y = –10(x – 5)
y = 10(x – 5)

Answer 1

Data on the missing table.
time (seconds)  x ; 0   1    2     3    4     5
height (meters) y ; 0  40  60  60  40  0
        
We simply substitute the values of x and y to see if they are equal.
x = 2 ; y = 60
y = -10(x) (x-5)
60 = -10(2) (2-5)
60 = -20 (-3)
60 = 60    CORRECT

y = 10(x) (x-5)
60 = 10(2) (2-5)
60 = 20 (-3)
60 = -60  INCORRECT

y = -10(x-5)
60 = -10(2-5)
60 = -10(-3)
60 = 30  INCORRECT

 y = 10(x-5)
60 = 10(2-5)
60 = 10(-3)
60 = -30 INCORRECT

The equation that models the height,y, x seconds after firing is y = -10(x) (x-5)

Answer 2

The table shows the approximate height of a projectile x (seconds) after being fired into the air, the equation models the height y & x seconds after firing is   $\rm y = -10(x)(x - 5)$

To check which of the following equations are true for the given statement we need to simplify conditions.

Given:

• x = represents seconds taken after  being fired into the air.
• y= represents height of a projectile.

TABLE :-

x= Time (in seconds)  :      0      1       2      3      4       5

y= Height (in meters)  :      0     40    60    60    40    0

       

We will now solve the given equations by substituting the values of x & y to check if they are equal i.e. if LHS= RHS

Lets take values from given table,

Time x = 2 & Height y = 60 in option (1) $\rm y = -10(x)(x - 5)$

$\rm y = -10(x) (x-5)\\60 = -10(2) (2-5)\\60 = -20 (-3)\\60 = 60$  

On solving, we get LHS=RHS , Therefore given equation (1) $\rm y = -10(x)(x - 5)$ is CORRECT

Therefore , $\rm y = -10(x)(x - 5)$  is the Correct equation that models the height-y & x-secongd after firing.

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