Use factoring to identify the x-intercepts of y = −3x^2 − 7x + 6.
To find the x-intercepts of the given quadratic equation, we need to find the values of x for which y equals zero. In other words, we need to solve the equation -3x^2 - 7x + 6 = 0.
To factor this quadratic equation, we need to find two numbers whose product is equal to -18 (-3 * 6) and whose sum is equal to -7. The numbers that satisfy these conditions are -9 and 2.
So, we can rewrite the equation as:
-3x^2 - 9x + 2x + 6 = 0
Now, we can factor by grouping:
(-3x^2 - 9x) + (2x + 6) = 0
-3x(x + 3) + 2(x + 3) = 0
(x + 3)(-3x + 2) = 0
Setting each factor equal to zero, we get:
x + 3 = 0 -3x + 2 = 0
x = -3 x = 2
Therefore, the x-intercepts of the given quadratic equation y = -3x^2 - 7x + 6 are x = -3 and x = 2.