HOW TO GRAPH A PARABOLA IN INTERCEPT FORM

Example 1 : 

Graph : y = -(x + 2)(x - 4)

Solution : 

The equation of the parabola is in intercept form

y  =  a(x - p)(x - q)

where a = -1, p = -2, and q = 4.

Because a < 0, the parabola opens down.

The x-intercepts occur at (-2, 0) and (4, 0).

The axis of symmetry lies halfway between these points, at x = 1.

So, the x-coordinate of the vertex is x = 1 and the y-coordinate of the vertex is :

y  =  -(1 + 2)(1 - 4)

=  -(3)(-3)

=  9

The graph of the equation is shown below.

Example 2 : 

Graph : y = (x + 2)(x - 3)

Solution : 

The equation of the parabola is in intercept form

y  =  a(x - p)(x - q)

where a = 1, p = -2, and q = 3.

Because a > 0, the parabola opens up.

The x-intercepts occur at (-2, 0) and (3, 0).

The axis of symmetry lies halfway between these points, at x = 0.5.

So, the x-coordinate of the vertex is x = 0.5 and the y-coordinate of the vertex is :

y  =  (0.5 + 2)(0.5 - 3)

=  (2.5)(-2.5)

=  -6.25

The graph of the equation is shown below.

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