Question

Here is it not sure if you will spot it

Answer 1

i dont understand your question

Answer 2

`f(x)=-5x^2+20x`

8.75 m

Explanation:

Given ordered pairs: (0, 0) (1, 16) (2, 20) (3, 15.5) (4, 0)

From inspection, we can see that the difference in the x-values is constant (they increase by 1 each time), yet the difference in the y-values is not constant. Therefore, the relation is not linear.

As the y-values increase from 0 to 20 and then decrease back to 0, the curve is likely to be a parabola opening downwards.

The x-intercepts are at x = 0 and x = 4, so this suggests that the axis of symmetry is x = 2, and so the vertex is (2, 20).

Creating an equation using the x-intercepts:

`f(x)=a(x-0)(x-4)` where
`a` is some constant

`\implies f(x)=ax(x-4)`

`\implies f(x)=ax^2-4ax`

Creating an equation using the vertex form:

`f(x)=a(x-2)^2+20`

`\implies f(x)=ax^2-4ax+4a+20`

Equating constants to determine a:

`4a+20=0 \implies a=-5`

Therefore, equation of best fit:
`f(x)=-5x^2+20x`

When x = 0.5:

`\implies f(0.5)=-5(0.5)^2+20(0.5)`

`=-1.25+10`

`=8.75`

Therefore, an estimate for the height of the rocket 0.5 s after it's launched is 8.75 m