Graphing Quadratics, Properties Of A Parabola Worksheet

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Prec Graphing Quadratics, Properties of a Parabola
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Graphing Quadratics, Properties of a Parabola
Quick Review
Standard Form
y = ax
2
+ bx + c
Vertex Form
2
y = a(x – h)
+ k
The axis of symmetry is a line that divides the parabola
into two symmetrical halves.
The vertex of a parabola is its turning point.  This is the
highest or lowest point on the parabola and always lies on
the axis of symmetry.
The parabola turns down (is concave down) if a < 0. 
The parabola turns up (is concave up) if a > 0. 
The x-intercepts of a parabola are its intersections with
the x-axis.  Find the x-intercepts by setting y = 0.
 
Solve the resulting quadratic equation either by
factoring or by using the quadratic formula.
Example Find the coordinates of the x-intercepts, the equation of the axis of symmetry, and the coordinates of the vertex, of the parabola whose equation is
2
y = 2x
– 6x -20.  Write the parabola in vertex form.
2
Solution     (a)  Set y = 0 and solve 0 = 2x
– 6x -20 by factoring.  We get
       2(x – 5)(x + 2) = 0 so x = 5 or x = -2.  Therefore, the coordinates of the x-intercepts are (5, 0) and (-2, 0).
(b)  The axis of symmetry must lie midway between the x-intercepts, so the equation of the axis is x = (5 – 2)/2 or x = 1.5.
2
      (c)   Since the vertex lies on the axis of symmetry, find its y-coordinate by substituting x = 1.5 to get y = 2(1.5)
– 6(1.5) – 20 = -24.5.  The coordinates of
the vertex are (1.5, -24.5).
2
      (d)   The vertex form of the equation is y = 2(x – 1.5)
– 24.5.
 
Problems
1.  For each equation of a parabola below:
      (i)   Find the coordinates of the x-intercepts
      (ii)  Find the equation of the axis of symmetry
      (iii) Find the coordinates of the vertex
      (iv) Write the equation in vertex form.
 
2
2
            a)   y = x
– 8x - 20                        b)  y = x
+ x – 2
 
2
2
            c)   y = 3x
– x - 10                        d)   y = 4x
+ 3x - 27
 
2.  Rewrite each of these quadratic equations in standard form.
 
2
2
            a)   y = 2(x – 4)
+ 5                      b)   y = -3(x + 2)
+ 2
 
3.  Use the Quadratic Formula to find the coordinates of the x-intercepts of each parabola.
 
2
2
            a)   y = 2x
– 7x - 20                     b)   y = x
+ 5x – 2
 
2
2
            c)   y = 3x
– x - 1                          d)   y = 4x
+ 3x - 7
 
 
file://D:\Documents and Settings\alipp\My Documents\Summer math website\Precalculus\TMP26...
8/16/2008

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