Question

Find the set of values if x for which each of the following is increasing. I know that answer is supposed to be x<-1.75 but I’m not sure how to get that and need help is possible. Thank you.

Answer 1

The general form of a quadratic equation is ax^2 + bx + c = y. From the equation for c, our a is -2, our b is -7 and our c is 5.

When a < 0, the function opens downward and has a maximum for its vertex.

When a quadratic function has maximum, its x values will always be increasing from negative infinity to the x-coordinate of the maximum (You can also simply write x < x coordinate of the maximum as you've already done).

We can find the x-coordinate of the maximum using the equation

`-b/2a`

Thus, since b is -7 and a is -2, we have

`-(-7)/2(-2)\\7/-4\\-7/4=-1.75`

This is how you get that the function is increasing from x < -1.75.

The green line in the attached picture also highlights the same idea.