SOLUTION: Determine whether the graph of y=3x^2+2x− 10 opens up or down and whether it has a maximum or minimum point.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Determine whether the graph of y=3x^2+2x− 10 opens up or down and whether it has a maximum or minimum point.       Log On


   

Question 457714: Determine whether the graph of y=3x^2+2x− 10 opens up or down and whether it has a maximum or minimum point.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Rule for y = ↏x² ± ↏x ± ↏
where there are numbers in the boxes and the sign ±
could either be + or -:

If the coefficient of x² is a POSITIVE number,
the graph looks like this:
graph%28100%2C+100%2C10%2C20%2C14%2C20%2C%28x-15%29%5E2%2B15%29
which opens UPWARD and has a MINIMUM point at 
the bottom. 

-------------------------------------------

If the coefficient of x² is a NEGATIVE number,
the graph looks like this
graph%28100%2C+100%2C10%2C20%2C-20%2C-14%2C-%28x-15%29%5E2-15%29
which opens DOWNWARD and has a MAXIMUM point at 
the top.

-------------------------------------------

Your equation is

y = 3x² + 2x − 10

and the coefficient of x² is 3, and 3 is a POSITIVE
number, so its graph is the first kind.  It opens 
UPWARD and has a MINIMUM point at the bottom. 

If fact here is the graph of your equation:

graph%28200%2C3200%2F7%2C-4%2C3%2C-11%2C5%2C3x%5E2%2B2x-10%29

Edwin