college algebra
posted by Jackie on .
I need help bad. Don't know which formula to use. Please explain step by step. 2x^212x+19. Find the interval where f is increasing and decreasing.

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^26x) + 19
= 2(x^26x+9) + 19  18
= 2(x3)^2 + 1
So, the vertex is at (3,1)
y decreases for x < 3
y increases for x > 3 
Vertex is b/2a
ax^2+by+c=0
or
(x2x1)/(y2y1)