A golfer aims for a hole that is 120 feet away and, when he hits the golf ball off the ground, its highest point reaches 80 feet up in the air. Noemi’s team is working together to write the quadratic equation to model the path of the golf ball in graphing form. She calculated the value of a = - 1/90 . Is she correct?

No she isn't. The value of is

Step-by-step explanation:

We know that all quadratic equation can be written in the following way :

(I)

Where and are real numbers.

I will attach a drawing with the quadratic graph to understand the situation.

We know by looking at the drawing and analyzing it that the parabola passes through the points : and

because we put our coordinates origin there.

because that's where the golf hole is.

And because we know that its highest point reaches 80 feet up in the air at the middle of the distance between its roots (property of a negative parabola).

Finally, we work with the three points and the equation (I) in order to find the values of and ⇒

The parabola passes through ⇒

⇒

⇒

The parabola passes through ⇒

⇒

(II)

The parabola passes through ⇒

⇒

(III)

Now if we use (III) in (II) ⇒

   ⇒

Finally the equation of the parabola is

Where the value of is

hiking down a winding trail.

step-by-step explanation:

she will travel a distance in the range of 3 - 11 miles