3x^2-6x-9
State the coordinates of the x-intercepts
show work.
-3 and 1
Y = 3x^2-6x-9 = 0.
A*C = 3 * -9 = -27. sum = 3 + (-9) = -6
= B.
3x^2 + (3x-9x) - 9 = 0.
Form two factorable binomials:
(3x^2+3x) - (9x+9) = 0.
3x(x+1) - 9(x+1) = 0.
(x+1)(3x-9) = 0.
x+1 = 0, X = -1.
3x-9 = 0, 3x = 9, X = 3.
Intercepts = -1, and 3.
To find the x-intercepts of the equation 3x^2 - 6x - 9, we need to solve for x when y (or the equation) equals zero. In other words, we are looking for the values of x that make the equation equal to zero.
Steps to find the x-intercepts:
1. Set the equation equal to zero:
3x^2 - 6x - 9 = 0
2. Now, we'll attempt to factor the quadratic equation. If it factors, it will help us determine the x-intercepts.
First, we look for the greatest common factor (GCF) of the equation. In this case, 3 is the common factor, so we can factor it out:
3(x^2 - 2x - 3) = 0
3. Next, we try to find two binomials that, when multiplied, give us the quadratic expression inside the parentheses. We need to find two numbers that multiply to -3 (the product of the last term) and add up to -2 (the coefficient of the middle term).
Factors of -3: -1, 1, -3, 3
Possible combinations: (-1, 3), (-3, 1)
After trying both combinations, we can rewrite the equation as:
3(x - 3)(x + 1) = 0
The x-intercepts occur when either (x - 3) equals zero or (x + 1) equals zero:
For (x - 3) = 0:
x = 3
For (x + 1) = 0:
x = -1
Therefore, the coordinates of the x-intercepts (or the solutions) are:
(3, 0) and (-1, 0)
So, the x-intercepts of the equation 3x^2 - 6x - 9 are (3, 0) and (-1, 0).