A flea jumps from the ground to a height of 30 cm and travels 15 cm horizontally from where it started. Suppose the origin is located at the point from which the flea jumped. Determine a quadratic function in vertex form to model the height of the flea compared to the horizontal distance travelled.

Step-by-step explanation:

Consider the equation that shows flea's motion is .

Since the origin is located at the point from where the flea jumped,

So,  passes through (0,0).

That is, (0,0) must satisfy ,

Now, it travels 15 cm horizontally from where it started.

That is,  passes through (15,0).

  (Because c=0)

 ...... (1)

Again, it jumps from the ground to a height of 30 cm,

So, the y-coordinate of vertex of is 30.

Now, the x-coordinate of vertex of the quadratic function must be half of the distance from its starting point to final point.

That is, x-coordinate of the vertex = = 7.5,

Thus, vertex = (7.5, 30)

(7.5, 30) must satisfy

That is,

               ...... (2)

Equation (1) - 2 × equation (2),

225a - 112.5a = -60

112.5a = -60

From equation (1),

Substitute the values of a, b and c in the quadratic equation ,

Which is the required quadratic equation.

trapezoid

step-by-step explanation:

first i plotted all my points on a grid graph

i made sure all of them were in the correct quadrant

then i saw it was a trapezoid or a quadrilateral