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| PAGE: 542 | SET: Exercises | PROBLEM: 51 |
The function is 
.
The standard form of quadratic function is 
.
Find the axis of symmetry.
Formula for the equation of the axis of symmetry is 
.
(Substitute 
and 
in the formula)
.
The equation for the axis of symmetry is 
.
Find the vertex.
Find the vertex, use the value of equation for the axis of symmetry as the 
- coordinate of the vertex.
Find the 
- coordinate.
(Original equation)
(Substitute in the original equation)
The vertex point is 
.
Determine whether the function has maximum or minimum value.
The value of 
(Positive), hence the graph of function opens upward and has a minimum value. The vertex is the minimum value.
The minimum value is 
.
The axis of symmetry divides the parabola into two equal parts.
If there is a point on one side, there is a corresponding point on the other side that is the same distance from the axis of symmetry and has the same 
- value.
Connect the points with a smooth curve.
.
The equation for the axis of symmetry is .
The vertex point is .
The vertex is the minimum value.
The graph of the function is
.
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