SPORTS When a golf ball is hit, the path it travels is shaped like a parabola. Suppose a

x2 + 10x + 24 = 0

x2 - 2x + 2 = 0

2x2 + 5x - 12 = 0

x2 + 8x = -15

FRAMING Julio is framing a picture in a 12-inch by 12-inch square frame. The frame is twice as wide at the top and bottom as it is at the sides. If the area of the picture is 54 square inches, what are the dimensions?

translated 4 units left and 2 units up

translated 5 units right and 3 units down

ARCHITECTURE The Connors plot their deck plans on a grid with each unit equal to 1 foot. They place the corners of a hot tub at (2, 5), (14, 5), (14, 17), and (2, 17). Changes to the plan now require that the hot tubs perimeter be threefourths that of the original. Determine possible new coordinates for the hot tub.

(-8, 0), (-2, 3)

(_3 5 , - _7 4), ( _1 4 , - _2 5)

(13, 24), (19, 28)

(-2, 10), (-2, 13)

(8, 5), (-9, 4)

(7, -3), (1, 2) 1

(_5 4 , _1 2), (_1 4 , _3 2)

How far away is the waterfall?

Marc wants to stop for lunch halfway to the waterfall. If the camp is at the origin, where should he stop?

(x - 1)2 = 12( y - 1)

y + 6 = 16(x - 3)2

x2 - 8x + 8y + 32 = 0

x = 16y

Write an equation for a parabola with vertex (0, 1) and focus (0, -1). Then graph the parabola.

SPORTS When a golf ball is hit, the path it travels is shaped like a parabola. Suppose a golf ball is hit from ground level, reaches a maximum height of 100 feet, and lands 400 feet away. Assuming the ball was hit at the origin, write an equation of the parabola that models the flight of the ball.

center (2, -3), radius 5 units

center (-4, 0), radius _3 4 units

endpoints of a diameter at (9, 4) and (-3, -2)

center at (-1, 2), tangent to x-axis

x2 + y2 = 169

(x + 5)2 + ( y - 11)2 = 49

x2 + y2 - 6x + 16y - 152 = 0

x2 + y2 + 6x - 2y - 15 = 0

WEATHER On average the circular eye of a tornado is about 200 feet in diameter. Suppose a satellite photo showed the center of its eye at the point (72, 39). Write an equation to represent the possible boundary of a tornados eye.

Write an equation for the ellipse with endpoints of the major axis at (4, 1) and (-6, 1) and endpoints of the minor axis at (-1, 3) and (-1, -1).

x2
16 + y2
25 = 1

(x + 2)
2 16 + ( y - 3)2
9 = 1

x2 + 4y2 - 2x + 16y + 13 = 0

The Oval Office in the White House is an ellipse. The major axis is 10.9 meters and the minor axis is 8.8 meters. Write an equation to model the Oval Office. Assume that the origin is at the center of the Oval Office.

Write an equation for a hyperbola that has vertices at (2, 5) and (2, 1) and a conjugate axis of length 6 units.

y2
4 - x2
9 = 1

16x2 - 25y2 - 64x - 336 = 0

(x - 2)
2 1 - ( y + 1)
2 9 = 1

9y2 - 16x2 = 144

MIRRORS A hyperbolic mirror is a mirror in the shape of one branch of a hyperbola. Such a mirror reflects light rays directed at one focus toward the other focus. Suppose a hyperbolic mirror is modeled by the upper branch of the hyperbola with equation y2
9 - x2
16 = 1. A light source is located at (-10, 0). Where should the light from the source hit the mirror so that the light will be reflected to (0, -5)?

-4x2 + y2 + 8x - 8 = 0

x2 + 4x - y = 0

x2 + y2 - 4x - 6y + 4 = 0

9x2 + 4y2 = 36

7x2 + 9y2 = 63

5y2 + 2y + 4x - 13x2 = 81

x2 - 8x + 16 = 6y

x2 + 4x + y2 - 285 = 0

ASTRONOMY A satellite travels in a hyperbolic orbit. It reaches a vertex of its orbit at (9, 0) and then travels along a path that gets closer and closer to the line y = 2
9 x. Write an equation that describes the path of the satellite if the center of its hyperbolic orbit is at (0, 0).

x2 + y2 - 18x + 24y + 200 = 0 4x + 3y = 0

4x2 + y2 = 16 x2 + 2y2 = 4

y < x y > x2 - 4

x2 + y2 9 x2 + 4y2 16

ARCHITECTURE An architect is building the front entrance of a building in the shape of a parabola with the equation y = -
1 10 (x - 10)2 + 20. While the entrance is being built the construction team puts in two support beams with equations y = -x + 10 and y = x - 10. Where do the support beams meet the parabola?