Use factoring to identify the x-intercepts of y = −3x^2 − 7x + 6.
To identify the x-intercepts, we need to find the values of x for which y equals zero.
So, we set y equal to zero and solve:
0 = -3x^2 - 7x + 6
To factor this trinomial, we need to find two numbers whose product is -18 (-3 * 6) and whose sum is -7.
The two numbers that satisfy this condition are -9 and 2.
Therefore, we can rewrite the equation as:
0 = -3x^2 - 9x + 2x + 6
Now, we can factor by grouping:
0 = (-3x^2 - 9x) + (2x + 6)
Factoring out the greatest common factor from the first two terms and the last two terms, we get:
0 = -3x(x + 3) + 2(x + 3)
Now, we can factor out the common binomial (x + 3):
0 = (x + 3)(-3x + 2)
Setting each factor equal to zero and solving for x, we get:
x + 3 = 0 or -3x + 2 = 0
Solving these equations, we find:
x = -3 or x = 2
Therefore, the x-intercepts of the equation y = -3x^2 - 7x + 6 are x = -3 and x = 2.