The path of a shot put released at an angle of 35° can be modeled by y=−0.01x2+0.7x+6, where x is the horizontal distance (in feet) and y is the vertical distance (in feet). find and interpret the coordinates of the vertex.
the coordinates of the vertex are ( , )
when the shot put is at its highest point, it is ( ) feet from its starting point and ( ) feet off the ground.

The vertex of an equation is the maximum or minimum point of the graph

The equation is given as:

For a quadratic equation:

The coordinates of the parabola is:

Where:

In

So:

Recall that:

So, we have:

This gives:

Hence, the coordinates of the vertex is: (35,18.25)

The starting point is when

So, we have:

The coordinates of the starting point is (0,6)

The distance between the starting point and the vertex is:

So, the interpretation is that:

When the shot put is at its highest point, it is 37.1 feet from its starting point and 35 feet off the ground.

Read more about vertex at:

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Coordinates of vertex (35,18.25)

The vertex is the highest point the shot put reached

When the shot put is at its highest point, it is 37.1 feet from its starting point and 35 feet off the ground.

Step-by-step explanation:

Given the equation as ;

y= −0.01 x² + 0.7x + 6

You can use the graph tool to view the turning point of the graph (vertex)

From the graph

Coordinates of vertex is (35,18.25)

x-intercepts are (-7.72,0), (77.72,0)

y-intercept is (0,6)

The distance from the highest point of the shoot put to its initial position is the distance of the line joining the vertex of the parabola and the initial position of shoot put.

Here you find the distance between point A(0,6) and B(35,18.3)

Apply the distance formula;

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47