Use the function to answer these questions

Question

Function- y=-3x²+8x+35

 

identify the axis of symmetry and the vertex

 

identify the maximum

 

find the x-intercepts by factoring

 

show the value of the discriminant supports your conclusion

 

describe the relationship of the x-intercepts to the axis of symmetry

Answer 1

 

y= -3x^2+8x+35

  = -3(x^2-8x-35)

   = -3(x-4/3)^2+121/3

 

So,vertex=(4/3,121/3)

Axis of symmetry =.   x= 4/3

Maximum point =. y = 121/3

 

x intercepts by factoring

 

y =-3x^2+8x+35

 

applying Discriminant formula

 

y= (-8+- sqrt(64+420))/-6

 

   (-8+22)/-6     &.  (-8-22)/-6

 

   -7/3.  &.  5

 

so  x  axis intercepts.  are. -7/3. &  5

 

 since axis of symmetry is x= 4/3

 

7/3+4/3  11/3

 

5-4/3=11/3

 

So, this justifies the x axis intercepts.