# data[].attributes.body
(click for fullscreen)

# data[].attributes.body
When we solve our quadratic with the quadratic formula, our two solutions are -46.75 and 363.75. The positive solution is the phone's location when it hits the ground, and the negative location is where the throw would have began if the phone was thrown from the ground.

# data[].attributes.body
We can create a quadratic equation in vertex form, because we know a point on the parabola and a vertex.
y=a(x-h)²+k

Vertex (h , k) = (111.6 , 155)
Known point (x , y) = y-intercept (0 , 68)

After Plugging in the Vertex:
68=a(0-111.6)²+155

Solving for a:
68=a(0-111.6)²+155
68=a(-111.6)²+155
68=12454.56a+155
-87=12454.56a
a=-.007

Vertex Equation:
y=-.007(x-111.6)²+155

Conversion to Standard Equation:
y=-.007(x-111.6)²+155
y=-.007(x-111.6)(x-111.6)+155
y=-.007(x²-111.6x-111.6x+12454.56)+155
y=-.007(x²-223.2x+12454.56)+155
y=(-.007x²+1.562x-87.182)+155
y=-.007x²+1.562x+67.818

# data[].attributes.body
The vertex of the quadratic is (111.6, 155). The vertex (or maximum, since the parabola opens down) is the highest point the phone reaches as it travels. We can find the vertex by using 155 inches as our Y coordinate and converting 9.3 feet to inches. 9.3 feet x 12 = 111.6 inches, our X coordinate.

# data[].attributes.body
The Y-Intercept of the quadratic is (0,68). This is derived from two knowns, 1: Dre's height, and 2: that he threw the phone from his head. In the context of the word problem, this is where the throw began.

# data[].attributes.body
Dre bought a brand new iPhone 7s! He pulls out his favorite headphones to listen to his favorite song. But, to his surprise, the iPhone 7s had no headphone jack! He got so frustrated he decided to throw his phone away.

# data[].attributes.body
Dre is 5 feet 8 inches tall. He throws his phone from his head. The phone flies 28 feet before shattering on the pavement. The phone reaches a maximum height of 155 inches when it is 9.3 feet away from Dre.