quadratic functions

standard form

f(x)= ax² + bx + c

properties of a quardratic function in standard form

• if a>0, vertex is minimum and curve concaves up (rightside up U)

• if a<0, vertex is maximum, curve concaves down (upside down U)

• axis of symmetry: x= -b/ 2a

• vertex: (-b/2a, f(-b/2a))

key features of quardratic functions

• x int is y=0, in parabolas called roots

• y int is y=c

• maximum occurs if a<0 at vertex

• minimum occurs if a>0 at vertex

• domain (-∞, ∞)

• range concave up: [f(-b/2a), ∞)

• range concaves down: (-∞, f(-b/2a)]

vertex form

f(x)= a(x-h)² + k

(h,k) is vertex

properties of quadratic function in vertex form

vertex is (h,k)

if a> 0 parabola concaves up

if a< 0 parabola concaves down

axis of symmetry: x= h

max/min at vertex (h,k)

key features of quadratic function in vertex form

x int y=0

y int x=0

domain (-∞,∞)

range (-∞,k] or [k, ∞)