Question

An equation that represents the path of a diver jumping off a diving board is y = –7x2 + 5x + 16. Graph this function from the point where the diver jumped to the point where they reach the water.

Answer 1

See explanation

Explanation:

An equation that represents the path of a diver jumping off a diving board is

`y = -7x^2 + 5x + 16.`

The diver jumped to the water when x = 0.

Then

`y=-7\cdot 0^2+5\cdot 0+16=16`

The jumper reached the water when y = 0, then

`-7x^2+5x+16=0\\ \\D=5^2-4\cdot (-7)\cdot 16=25+448=473\\ \\x_(1,2)=(-5\pm√(473))/(-14)`

So, point where the jumper reached the water is

`\left((5+√(473))/(14),0\right)\approx (1.93,0)`