Determine whether f(x) =3x^2+9x-2 has a maximum of a minimum value and find that value by hand.

f(x) =3x^2+9x-2 has a minimum value. Minimum value of f(x) is

Solution:

Given, equation is

We have to find whether given equation has maximum or minimum for the given equation.

Now, we know that, f(x) is a quadratic equation and coefficient has is positive, then its graph is upward parabola. Which means that it will have minimum

The minimum value upward parabola will be its vertex.

So, let us convert f(x) into general form. That is,

where a is constant and (h, k) is vertex

Taking "3" as common from first three terms,

Now multiply and divide “2” with “3x” for easier calculations

So, by comparison with general form we get,

idk

step-by-step explanation:

use that smart brain

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!