Page 66 - Math SL HB Sem 1

F{JNCTTONS, EQUA'rrONS ,INEQUAT,ITIES

6. 'I}IE QUADRATIC F'UN(]TION

A quadratic function has the general form
/(x) =ax2 +bx+c,a * 0 anda,b,c e R. All
quadratic lunctions have parabolic graphs and have a vertical axis of symmetry.

l. If a > 0 the parabola is concave up :

2. lf a < 0 the parabola is concave down:

General Properties of the graph of

J.U) = ttx' +bx+c,a + 0

l. y-intercept

This occurs when x=0,sothat y= (0) o($)'z + r(0) + c =c.Thatis, the curve passes
=
"f
through the point (0, c)
2. x-intercept(s)

l'his occurs where /(x) = 0 . Therefore we need to solve ax2 + bx + c = 0 . To solve wc
either factorize and solve, or use the quadratic formula, which rvoulcl provide the
-b-t b2 4ac
-
solution(s) x =
2u

v
f(x) = u*z + bx + c,a > 0
axis ofi symmetry

-b+ b2 4ac
x
2a
0 -r

(n
-h- b2 4ac i __ (_L\
-
f
2rt I \ 2a)
\ 2o'
Vertex
b
2a

l- 19