identify the vertex, axis of symmetry, maximum and minimum value and value of parabola. Y=X^2 +6X+7

Question

IDENTIFY THE PARTS 

Answer 1

Faith,

 

The axis of symmetry is the line x = -3.

 

The minimum value is -2 and occurs at the point (-3, -2) which, of course, is also the vertex.

 

Parabola Vertex Focus Calculator Formulas

(Y = aX2 + bX + c, a≠0)

1. Focus X = -b/2a

2. Focus Y = c - (b2 - 1)/4a

3. Vertex X = -b/2a

4. Directrix Y = c - (b² + 1)/4a

5. X Intercept = -b/2a ± √(b² - 4ac)/2

Answer 2

∞

 

                             

 Y = X² + 6X +7

 

      X          = -b/ 2a = -6/ 2 = -3

        vertex

 

      Y            = ( -3) ² + 6( -3) + 7 = -2

        vertex

 

        Vertex = ( -3, -2)

 

          Minimum value occurs at vertex = -2

         

       Domain of function( -∞, +∞) , the function does not have a bounded maximum

 

       f( x) = aX² + bx + c     is a parabola

 

           for a>0  the parabola opens upward and minimum value is at X= -b/2a, and  vertical line of

               X=-b/2a is axis of symetry

              a<0 , then parabola opens downward and everything takes place the same way but at maximum

                        value.