The path of a skateboarder can be modeled by the equation (x – 4)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?
Maximum height 4 feet; horizontal distance 12 feet
Maximum height 5 feet; horizontal distance 10 feet
Maximum height 9 feet; horizontal distance 12 feet
Maximum height 9 feet; horizontal distance 10 feet

Question

contestada

Respuesta :

Polyblock Polyblock · Answer 1 · 2021-10-25T23:50:26+02:00

Answer:

Maximum height 9 feet; horizontal distance 10 feet

Step-by-step explanation:

First, let's get the distance out of they way

When the skateboard lands, her height will be at 0 feet, so y has to equal 0

(x - 4)² = -4(0 - 9)

(x - 4)² = -4(-9)

(x - 4)² = 36

Square root both sides

√(x - 4)² = √36

x - 4 = 6

Note that x - 4 = -6 is also possible

Add 4 to both sides

x - 4 = 6

+ 4 + 4

x = 10

Note that x = -2 is also an answer. but not valid

To find the max height

Remember our zeros? x = -2, x = 10

The number in the middle would be 4

Plug 4 in place of the x in the original equation

(4 - 4)² = -4(y - 9)

(0)² = -4(y - 9)

0 = -4(y - 9)

You can divide both sides by 4

0/4 = (-4(y - 9))/4

0 = y - 9

+ 9 + 9

y = 9

Vertex is (4,9); or in other words, 9 feet is the max height