Question

When a ball is tossed into the air, it's height is a quadratic function of time. One student models the height of the ball as h(t)= -16t^2. Another student models it as h(t)= -16t+10. Could both models be correct? Explain.

Answer 1

Height equation for first student is correct while that of second student is incorrect.

Explanation:

Given that the function of height should be quadratic function.

Standard form of Quadratic function is given as,

`f\left(x\right)=ax^2+bx+c`.

Degree of quadratic function is 2.

Equation of height for first student is given as
`h\left(t\right)=-16t^(2)`

Since, above equation has degree 2 and equation is in quadratic form with value of b and c as 0.

Therefore, height equation for first student is correct.

Equation of height for second student is given as
`h\left(t\right)=-16t+10`.

Since the degree of above equation is 1, hence it cannot be the quadratic function. Hence second equation is not an quadratic function.

Therefore, height equation for second student is incorrect.