posted by Jackie on .
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.
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
Vertex is -b/2a