Mat 101

Describe in words the graph of each of these curves below. Include in your description the shape, along with other possible relevant information such as length, width, and center points.

a. Y = 3X2 : The graph has the shape of a parabola. It’s vertex is (0,0), and it is stretched by 3 when compared to the graph of x^2.

b. (X-1)2 + (Y-8)2 = 16 This graph has the shpe of a circle. It’s center is (1,8) with radius 4

c. (X+2)2 + (Y-4)2 = 36 This graph has the shape of a circle. It’s center is (-2, 4) with radius of 6

d. Y = X2 + X This graph has the shape of a parabola. It has x-intercepts at the origin and at x=1. Only y-intercept is at the origin. The parabola opens up with vertex at (1/2, -1/4)

Part II

Find the equation for each of the following items below:

a. A line that passes through (6,26) and has a slope of 3.

y= Slope x + c

y=3x+c

26 = 3*6+c

26=18+c

26-18=c

8=c

y =3x+8

b. A line that passes though the points (5,5) and (10,20)

Slope = change in y / change in x = (20-5)/(10-5) = 5/15 =3

y = 3x+c

5 = 3*5+c

5 =15+c

5-15=c

-10=c

y = 3x-10

c. A line that passes through (9,25) and has a slope of -3.

Slope =-3x+c

25 =-3*9+c

25=-27+c

25+27=c

52=c

y = -3x+52

d. A line that passes through (1,1) and is perpendicular to the line 4x+6Y=18.

4x+6y=18

6y = -4x + 18

y = -2/3x+3

Slope = -2/3

any slope which is perpendicular to -2/3 equals

-2/3M = -1

M = 3/2

perpendicular line y = (3/2)x + c

1 = (3/2)*1+c

1-3/2=c

2/2-3/2=c

-1/2=c

y = (3/2)x-1/2 OR -3x+2y = -1

e. A circle with a radius of 4 and a midpoint at (2,2)

(x-2)² + (y-2)² =4²

(x-2)² + (y-2)² =16

Part III

Solve for the following items:

a. The point on the x-axis that is equidistant (equal distance) from (8,4) and (-4,2).

(x,0) represents point putting in equation with points (-4,2) & (8,4)

(-4-x)² + (2-0)² = (8-x)² + (4-0)²

16+8x+x² +4 = 64-16x+x²+16

20+8x+x²=80-16x+x²

8x+16x= 80-20

24x=60

x=60/24

x=2.5

location of point is...