Page 66 - Math SL HB Sem 1

FUNC't-IONS, EQUATIONS, INE QUALITIES

6. 'rllE QUADI{A'r'IC F-UNCTION

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

/(r)-a*'+bx+c,a + 0

l. y-intercept

This occurs when x = 0, so that y=f(0)=a(o)'z+6(0)+c=c.Thatis,rhecurvepasses
through the point (0, c)

2. x-intercept(s)
'['his
occurs where /(-r) = 0 . Therefore we need to solve ar2 + bx + c = 0 . To solve we
either factorize and solve, or use the <luadratic formula, which woukl provide the
-b+ b' 4ac
solution(s) -r =
2a

v
f(x): u*u + bx + c,a > 0

ax is of symmetry

-b+J;' - 4ac

2a
0 -r

-b- b' 4ac (h
a l-a' (*)
2a

Vertex
b
2a

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