Page 67 - Math SL HB Sem 1

I,-I]NCTI()NS riQriA'ilo NS, tNIrQtJAt,t'ilES
,

l. Axis of symmetry
a,
This occurs ut -. = -
2a
4. Vcrtex (turning point)

I'he vertex occurs when ,=- b
Then, to find the y vatue, find t(-
2a *)

Sketchin q the aPh of a ouadratic function

I."vo methods for sketching the graph of
f(x) - ax2 + bx + c.a + 0 are :

iucthod 1: l'he intercept method
i.e; expressing
f$)= or, +bx+c,a*O inthe form f(x)_ a(x p)(x q)
-
This involves;

Step l. Finding the -r -intercepts
[by solving ax2 + bx + c = 0]
Step 2. Finding rhe y - intercepts [finding /(0)]
Step 3. Sketch parabola passing trough the three points.

lVltthod 2:
f =
The turning-point form i.e. expressing (x) rrr, + bx + c,a + 0 in the form
"f(x)=a(x-h)'1 + k
This involves;

Step l. Expressing f(x)= axz +bx+c,a+0 i. the lorm a(x_h)2 +l
Iby completing the square]
Step 2. Use the turning point (h, k)
Step 3. Finding the y - interceprs [finding /(0)]

Step 4. Sketch parabola passing through the two points.

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