To determine the intervals on which the quadratic function is positive, we need to find the x-values for which the function outputs positive values (y > 0).
We can start by factoring the quadratic equation:
y = 3x^2 - 20x + 12
= (x - 2)(3x - 6)
Setting the equation equal to zero to find the x-intercepts:
x - 2 = 0
x = 2
3x - 6 = 0
3x = 6
x = 2
Now, we can determine the signs of the quadratic function in the intervals formed by the x-intercepts:
Interval 1: (-∞, 2)
Choosing any value less than 2, e.g., x = 0:
y = 3(0)^2 - 20(0) + 12
y = 12
Since y is positive, the quadratic function is positive in this interval.
Interval 2: (2, +∞)
Choosing any value greater than 2, e.g., x = 3:
y = 3(3)^2 - 20(3) + 12
y = 9 - 60 + 12
y = -39
Since y is negative, the quadratic function is not positive in this interval.
Therefore, the quadratic function y = 3x^2 - 20x + 12 is positive in the interval (-∞, 2).
identify the intervals on which the quadratic function is positive
y=3x^2 -20x+12
1 answer