Sammy's Shot by Emily

The Problem

maye1592 — 2016-12-06 20:36:11 UTC

The AH mules basketball team is down by 2 points. Sammy gets the ball with 3 seconds left. Sammy shoots from the 3 point line, which is 19.75 ft from the basket. The ball leaves Sammy's hands at 5 and 2/3 ft above the ground at his head. The maximum height of the ball is 5 ft above the basket, which is 10 ft tall and the ball peaks at 14.8 ft away from Sammy. Write an equation using matrices to represent this quadratic situation and solve for the y intercept, vertex, and solutions that satisfy the equation.

Brainstorming

maye1592 — 2016-12-06 20:38:20 UTC

2016-12-07 23:14:41 UTC

Matrix Equation and solutions through quadratic formula.
Points chosen for matrix are point in drawing to the right.
x={25.127, -2.717}

sam72 — 2016-12-08 02:37:44 UTC

Y Intercept

maye1592 — 2016-12-08 02:38:58 UTC

(0,5 2/3)- The y intercept is where the ball starts moving to the basket. It is not (0,0) because Sammy releases the ball at at 5 and 2/3 ft tall.

Work Cited

maye1592 — 2016-12-08 03:08:42 UTC

For basketball picture
Basketball. Digital image. Prince George's County Boys and Girls Club. Prince George's County Boys & Girls Club, 2016. Web. 7 Dec. 2016. .

maye1592 — 2016-12-08 03:12:01 UTC

Vertex

maye1592 — 2016-12-08 03:14:07 UTC

(14.8,15)-The vertex is the highest point the ball reaches. As Sammy's shot moves toward the basket it takes about 3/4 of the 19.75 ft to reach it's highest point. That is why the x value is 14.8.

2016-12-08 03:23:07 UTC

-2.717 represents the spot if Sammy had shot from ground level, and 25.127 marks the spot the ball would hit if it were to continue on after going through the net.