Find the equation of a circle with the following radii and c

Find the equation of a circle with the following radii and centers. Center: (1, 5) Radius = 2 Center: (-2, 4) Radius = 4 Solve the equations for the unknown. You must show your work. Leave answer in simplified fractions. |3x - 1| > 1/8 |2x + 1| lessthanorequalto 5/7 Find the vertex of the quadratic functions below. Show your work. f(x) = 2x^2 - 3x + 10 g(x) = (2x + 1)(3x - 2) h(x) = -4(x - 1)^2 + 3

Solution

1) centre (1, 5) , radius = 2

Standard equation of circle with centre (h, k) and radius r

(x- h)^2 + (y -k)^2 = r^2

So, (x -1)^2 + ( y-5)^2 = 4

2) centre ( -2, 4) , radius = 4

(x +2)^2 + ( y- 4)^2 = 16

3) Solve inequality :

|3x -1| > 1/8

3x -1 > 0 ; 3x -1> 1/8

x>9/8*3 ; x> 3/8

(3x -1) <0

-3x +1 > 1/8

3x < 1-1/8 = 7/8

Solution: (3/8 , 7/8)

5) f(x) = 2x^2 - 3x   + 10

Vetex of quadratic function is given by : ax^2 +bx +c

x = -b/2a and y = f(-b/2a)

So, x = - (-3)/2*2) = 3/4

f( 3/4) = 2(3/4^2 - 3(3/4) + 10

= 3/8 - 9/4 +10

= (3 -18 +80)/10 = 65/10 = 13/2

Vertex ( (3/4 , 13/2)