Question

Peter hits a golf ball from a 210 m high hill. The height of the ball at any time t can be modelled by the equation
h(t)=−6t2+12t+210.
Which of the following represents its factored equivalent?

Answer 1

To find the factored equivalent of the equation, we need to factorize the quadratic equation -6t^2 + 12t + 210.

First, let's divide the equation by -6 to simplify it:
h(t) = -6t^2 + 12t + 210
Dividing by -6, we get:
h(t) = t^2 - 2t - 35

Now, we need to find two numbers whose sum is -2 and whose product is -35. The numbers that satisfy these conditions are -7 and +5. Therefore, we can factorize the equation as:
h(t) = (t - 7)(t + 5)

Thus, the factored equivalent of the equation is (t - 7)(t + 5).