I need help bad. Don't know which formula to use. Please explain step by step. 2x^2-12x+19. Find the interval where f is increasing and decreasing.

Answer 1

If you are confused by formulas, it indicates you don't really understand the concepts. Let's start from scratch.

You know the graph is a parabola, which has a vertex.
Since the coefficient of x^2 is positive, the vertex is at the minimum value of y.

So, left of the vertex y is decreasing, and on the right, it is increasing.

So, where is the vertex?

y = 2x^2 - 12x + 19
= 2(x^2-6x) + 19
= 2(x^2-6x+9) + 19 - 18
= 2(x-3)^2 + 1

So, the vertex is at (3,1)
y decreases for x < 3
y increases for x > 3

Answer 2

Vertex is -b/2a

ax^2+by+c=0

or

(x2-x1)/(y2-y1)