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The path of a skateboarder can be modeled by the equation (x – 3)2 = –4(y – 9), where distance is in feet and air resistance is insignificant. If the skateboarder makes a jump from a ramp at x = 0, what is her maximum height and how far is she horizontally from the end of the ramp when she lands?

Respuesta :

Answer:

The correct answer would be: "Maximum height 9 feet; horizontal distance 9 feet".

Step-by-step explanation:

I know this not only because I already took the test, BUT by graphing the equation (you can use graphing apps) it'll give you the answer.

varshamittal029

Her maximum height is 9 feet & she is horizontally 9 feet from the end of the ramp when she lands.

What is skateboarders maximum height ?

The path of the skateboarder can be modelled by the equation,

(x-3)² = -4(y-9)

Now, from the equation, solving y,

(x-3)² = -4(y-9)

⇒ y-9 = -[tex]\frac{1}{4}[/tex](x-3)²

⇒ y = -[tex]\frac{1}{4}[/tex](x-3)² + 9

∴ Maximum height is 9 feet.

How far is she horizontally from end of ramp ?

We have to take y = 0,

Now, -[tex]\frac{1}{4}[/tex](x-3)² + 9 = 0

        ⇒ -(x²-6x+9)+36 = 0

        ⇒ -x²+6x-9+36 = 0

        ⇒  x²-6x-27 = 0

        ⇒ x²-9x+3x-27 = 0

        ⇒ (x-9)(x+3) = 0

        ⇒ x = 9 or x = -3

Neglecting the negative value we get, x = 9

So, Her horizontal distance from end of the ramp is 9 feet.

Learn more about quadratic problems here :

https://brainly.com/question/16073165

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