Consider the graph of the quadratic function y = 3x2 - 3x - 6. What are the solutions of the quadratic equation 0 = 3x2 - 3x - 6?

Y = 3x^2 - 3x - 6 {the x^2 (x squared) makes it a quadratic formula, and I'm assuming this is what you meant ... }

This is derived from:

y = ax^2 + bx + c

So, by using the 'sum and product' rule:

a * c = 3 * (-6) = - 18

b = - 3

Now, we find the 'sum' and the 'product' of these two numbers, where b is the 'sum' and a * c is the 'product':

The two numbers are: - 6 and 3

Proof:

-6 * 3 = - 18 {product}

-6 + 3 = - 3 {sum}

Now, since a > 1, we divide a from the results

-6/a = - 6/3 = - 2

3/a = 3/3 = 1

We then implement these numbers into our equation:

(x - 2) * (x + 1) = 0 {derived from 3x^2 - 3x - 6 = 0}

To find x, we make x the subject of 0:

x - 2 = 0

OR

x + 1 = 0

Therefore:

x = 2

OR

x = - 1

So the x-intercepts of the quadratic formula (or solutions to equation 3x^2 - 3x - 6 = 0, to put it into your words) are 2 and - 1.

We can check this by substituting the values for x:

Let's start with x = 2:

y = 3 (2) ^2 - 3 (2) - 6

= 3 (4) - 6 - 6

= 12 - 6 - 6

= 0 {so when x = 2, y = 0, which is correct}

For when x = - 1:

y = 3 (-1) ^2 - 3 (-1) - 6

= 3 (1) + 3 - 6

= 3 + 3 - 6

= 0 {so when x = - 1, y = 0, which is correct}