Page 67 - Math SL HB Sem 1

_ r-ullIlqrys, Eau4l!e!!s, r NEQUALn_|ES

l. Axis of symmetry
a.
This occurs at .. = -
2a
4. Vertex (turning point)

The vertex occurs when, = - Then, to fi nd the y _ valu r*
* ", f (_ *)

Sketchin q the raph of a qua dratic function

'l'rvo
methods for sketching the graph of
/(.r) = axz + bx + c,a * 0 are:,
Method l: The intercept method

i.e; expressing
f(x)=ax'+bx+c,o*O inrhe form f(x)= a(x_ p)(r _ q)
This involves;

Step l. Finding the x -intercepts
[by solving ax? + bx+c =01
Step 2. Finding thc y - intercepts [finding /(0)]
Step 3. Sketch parabola passing trough the tkee points_

Nlcthod 2: The turning-point form i.e. expressing
.f(r) = o*, + bx + c, a + 0 inthe form
f(x)=a(x'h)'1 + k
'fhis
involves;

Step l. Expressing
f(x) = ax2 +bx+c,o+0 in the form a(x_h)2 +y
Iby completing the square]
Step 2. Use the tuming point (h, k)
Step 3. Finding the 7- interceprs [fincling /(0)]

Step 4. Sketch parabola passing through the two points,

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