## Pages

### Graph y = (x - 1)(x - 4)

 Graph of y = (x - 1)(x - 4)
Comparing the equation with intercept form y = a(x - p)(x - q), p = 1 and q = 4. So the x-intercepts are (1, 0) and (4, 0).

Let the vertex be (h, k), then h = (p + q)/2 = (1 + 4)/2 = 5/2,

k = (5/2 - 1)(5/2 - 4)
k = (3/2)(-3/2)
k = -9/4

Therefore the vertex is (5/2, -9/4). Now plot the vertex and x-intercepts and join them with a free hand curve

### Graph y = 3(x - 6)(x - 3)

 Graph of y = 3(x - 6)(x - 3)
Comparing the equation with intercept form y = a(x - p)(x - q), p = 6 and q = 3. So the x-intercepts are (6, 0) and (3, 0).

Let the vertex be (h, k), then h = (p + q)/2 = (6 + 3)/2 = 9/2,

k = 3(9/2 - 6)(9/2 - 3)
k = 3(-3/2)(3/2)
k = -27/4

Therefore the vertex is (9/2, -27/4). Now plot the vertex and x-intercepts and join them with a free hand curve

### Graph y = -2(x - 4)(x - 5)

Comparing the equation with intercept form y = a(x - p)(x - q), p = 4 and q = 5. So the x-intercepts are (4, 0) and (5, 0).
 Graph y = -2(x - 4)(x - 5)

Let the vertex be (h, k), then h = (p + q)/2 = (4 + 5)/2 = 9/2,

k = -2(9/2 - 4)(9/2 - 5)
k = -2(1/2)(-1/2)
k = 1/2

Therefore the vertex is (9/2, 1/2). Get some more points on the parabola by making table of x-y values

 x Y = -2(x - 4)(x - 5) 2 -12 3 -4 6 -4 7 -12

Now plot the vertex and x-intercepts and join them with a free hand curve

### Graph y = (x + 2)(x + 3)

Comparing the equation with intercept form y = a(x - p)(x - q), p = -2 and q = -3. So the x-intercepts are (-2, 0) and (-3, 0).

Let the vertex be (h, k), then h = (p + q)/2 = (-2 + -3)/2 = -5/2,

k = (-5/2 + 2)(-5/2 + 3)
k = (-1/2)(1/2)
k = -1/4

Therefore the vertex is (-5/2, -1/4). Now plot the vertex and x-intercepts and join them with a free hand curve.  Get some more points on the parabola by making table of x-y values

 x y = (x + 2)(x + 3) -1 2 -4 2 0 6 -5 6
Now plot the vertex and x-intercepts and join them with a free hand curve
 Graph of y = (x + 2)(x + 3)