If we are given sufficient information on or about a graph, we can determine the quadratic function in
whatever form is required.
Example 20 Self Tutor
Find the equation of the quadratic function with graph:
ab
a Since thex-intercepts are¡ 1 and 3 ,
y=a(x+ 1)(x¡3).
The graph is concave down, so a< 0.
When x=0, y=3
) 3=a(1)(¡3)
) a=¡ 1
The quadratic function is
y=¡(x+ 1)(x¡3).
b The graph touches thex-axis at x=2,
so y=a(x¡2)^2.
The graph is concave up, so a> 0.
When x=0, y=8
) 8=a(¡2)^2
) a=2
The quadratic function is
y=2(x¡2)^2.
Example 21 Self Tutor
Find the equation of the quadratic function with graph:
The axis of symmetry x=1lies midway between thex-intercepts.
) the otherx-intercept is 4.
) the quadratic has the form
y=a(x+ 2)(x¡4) where a< 0
But when x=0, y=16
) 16 =a(2)(¡4)
) a=¡ 2
The quadratic is y=¡2(x+ 2)(x¡4).
E Finding a quadratic from its graph
-2
y
x
x=1
16
O
-2
y
x
x=1
16
3 units 3 units
O
y
x
3
-1 3
O
y
2 x
8
O
Quadratics (Chapter 3) 87
4037 Cambridge
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Y:\HAESE\CAM4037\CamAdd_03\087CamAdd_03.cdr Thursday, 3 April 2014 4:46:38 PM BRIAN