Question

identify the intervals on which the quadratic function is positive

y=2x^2 -15x+18

Answer 1

To determine the intervals on which the quadratic function is positive, we need to find the x-values for which the function's y-values are greater than zero.

To do this, we can set the quadratic function equal to zero and solve for x:

2x^2 - 15x + 18 = 0

Factoring the quadratic equation, we have:

(2x - 3)(x - 6) = 0

Setting each factor equal to zero gives us:

2x - 3 = 0 or x - 6 = 0

Solving these equations, we find:

2x = 3 -> x = 3/2
x = 6

Now we have three critical values: x = 3/2, x = 6, and the vertex of the quadratic function.

We know that the quadratic function is positive when the value of y is greater than zero.

To find the intervals on which the quadratic function is positive, we only need to consider the intervals between the critical values.

In this case, we have the following intervals:

(-∞, 3/2), (3/2, 6), (6, ∞)

Therefore, the quadratic function y = 2x^2 - 15x + 18 is positive on the intervals (-∞, 3/2) and (6, ∞).