I am practicing finding y and x intercepts of a parabola. My equation is y = x^2 - 2x - 3
My y intercept is (0 , -3)
When I factor the equation I get (x + 1)(x -3) so my x intercepts would be (-1 , 0) and (3, 0)
However, when I use the quadratic formula to get my x intercepts, I get (1, 0) and (-3 ,0), just the opposite!
What am I doing wrong?
This happened again with another one
3x^2 + 5x - 2
Y intercept is (0, -2)
Factored is (3x - 1)(x + 2)
So x intercepts are (1/3, 0) and (-2, 0)
When I did the quadratic formula I got
X = -5 plus or minus 1/ 6
x = -5 + 1/6 = -4/6 = = -1/3. But in the factored form I got positive 1/3
Then x = -5 - 1/6 = -6/6 = -1 and in the factored form I got -2
And I did check my factoring and it came out correctly!
Where am I going wrong?
y = x^2 - 2x -3.
X = (2 +- sqrt(4 +12))/2 = 3 and -1.
y = 3x^2 + 5x - 2.
X = (-5 +- sqrt(25 + 24))/6 = 1/3 and -2.
It seems like there might be a mistake in your factorization or when applying the quadratic formula. Let's go through the correct steps to find the x-intercepts of the parabola with the equation y = x^2 - 2x - 3.
To find the y-intercept, you correctly determined that it occurs when x = 0. Plugging x = 0 into the equation, we get:
y = (0)^2 - 2(0) - 3 = -3
So the y-intercept is (0, -3).
Now, to find the x-intercepts, you initially factored the quadratic equation incorrectly. The correct factorization is (x + 3)(x - 1). Let's check:
Setting y = 0 in the equation:
0 = (x + 3)(x - 1)
This equation will be true if either (x + 3) = 0 or (x - 1) = 0.
For (x + 3) = 0, we have x = -3.
For (x - 1) = 0, we have x = 1.
Therefore, the x-intercepts are (-3, 0) and (1, 0).
So, there was a mistake in your factorization. The correct x-intercepts are (-3, 0) and (1, 0). The (-1, 0) and (3, 0) that you mentioned do not represent the x-intercepts of this specific parabola. Double-check your factorization and calculations to ensure accuracy.