Graph `y = (x  1)(x  4)`
Graph of `y = (x  1)(x  4)` 
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 xintercepts and join them with a free hand curve
Graph `y = 3(x  6)(x  3)`
Graph of `y = 3(x  6)(x  3)` 
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 xintercepts 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 xintercepts are `(4, 0)` and `(5, 0)`.
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 xy values
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 xy values
x

Y = 2(x  4)(x 
5)

2

12

3

4

6

4

7

12

Now plot the vertex and xintercepts 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 xintercepts 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 xintercepts and join them with a free hand curve. Get some more points on the parabola by making table of xy values
Now plot the vertex and xintercepts and join them with a free hand curve
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 xintercepts and join them with a free hand curve. Get some more points on the parabola by making table of xy values
x

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

1

2

4

2

0

6

5

6

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