Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range.

Question

y=-5x(2)+3x+10 state the doain and range also pls

Answer 1

you should know the following facts, regardless of any calculator consideration.

1. the x coordinate of the vertex of a parabola is x = -b/(2a)

2. the y coordinate of the vertex is obtained by substituting the above x value in the function definition.

3. if a (in this case it's -5) < 0 then the vertex represents the highest point of the graph, so then the range is (-infinity, ymax).

4. if a > 0, then the vertex represents the lowest point of the graph, so then the range is (ymin, infinity)

5. for all quadratic graphs (parabolas), the domain is ALL REALS.

Answer 2

Do I understand correctly that you meant -5X² + 3X + 10 ?

If so, this is a fairly quick one. Remember that the domain is any input that will produce a sane answer (in other words, nothing illegal). Is there anything you can't multiply by -5 or 3? Is it ever impossible to square a number or add ten? "No" to all of the above, so the domain on all polynomials is all real numbers.

Range? That one takes a tiny bit of work. The maximum or minimum of a quadratic is always the vertex. If the curve has a leading negative, it points down and has a maximum. Likewise, a leading positive means it points up and has a minimum. Yours points down. Let's find that vertex!

Remember the formula:

 

X = - b                  Where "a" is the coefficient of X² and "b" is the coefficient of X.

       2a                   In this case, that gets you...

 

X = -3      =  -3   = 3       Plug that into the quadratic function

      2(-5)      -10     10

 

and you will find the maximum value Y can have. Your range will run from -∞ to that value