Equation of a Circle Finding the center and

Equation of a Circle Finding the center and radius of any given circle or equation of a circle

Different form of Quadratic functions • Standard Form • F(x) = ax 2 + bx + c • Vertex Form • F(x) = a(x – h)2 + K • Factor Form • F(x) = (x + b)(x + d)

Standard Form What is it good for? • Identifying Minimum or Maximum • Y-intercept recognition • Example: • Y= 3 x 2 – 4 x + 5 • Y= -4 x 2 + 5 x - 8

Vertex form: what is it good for? • Identify Vertex • Axis of Symmetry • Example: • F(x) = 3(x-4)2 + 5 • F(x) = -5(x + 7)2 - 9

Factor Form: What is it good for? • Identifying zeros • Example: • Y = 2(x -3)(2 x + 5) • H(x) = -7 (3 x + 1) (x + 2)

What can you tell me about a circle? • Radius • Center • Not a function • Not a Polygon • Circumference • Area

Identify Radius and Center of the given:

Equation of a Circle • (x – + = • (h, k) is the Center • r is the radius 2 h) 2 (y-k) 2 r

Identifying Radius and Center • (x – 5)2 + (y - 9)2 = 25 • Center__________ Radius _________ • (x – 3)2 + (y +4)2 = 16 • Center__________ Radius _________ • x 2 + (y +3)2 = 12 • Center__________ Radius _________ • x 2 + y 2 = 72 • Center__________ Radius _________

Writing Equations Given Center and Radius:

How do we find radius and Center if equation is not in standard form? • X 2 + 8 x + y 2 + 6 y = -1 • You Try: X 2 - 4 x + y 2 - y = -1

How do we find radius and Center if equation is not in standard form? • 4 X 2 + 8 x + 4 y 2 - 12 y = 8 • You Try: X 2 + y 2 = -4 x + 2 y

Any Questions: