How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #y=x^2+6x+2#?

Question

Abigail Allen · Accepted Answer

#x=-3" " # is the axis of symmetry

the vertex of the parabola is at #(h, k)=(-3, -7)# by the formula #h=-b/(2a)# and #k=c-b^2/(4a)# from the given #y=x^2+6x+2# #a=1#, #b=6#, and #c=2# #h=-b/(2a)=-6/(2*1)=-3# #k=c-b^2/(4a)=2-6^2/(4*1)=2-36/4=2-9=-7# The minimum point is the vertex #(-3, -7)# graph{y=x^2+6x+2 [-13.58, 6.42, -8.6, 1.4]} and clearly #x=-3# a vertical line which passes thru #(-3, -7)# is the line of symmetry. God bless....I hope the explanation is useful.

Hazel Anglin · Answer

undefined To find the axis of symmetry of a quadratic function $ y = ax^2 + bx + c $, use the formula: $ x = -\frac{b}{2a} $. For the function $ y = x^2 + 6x + 2 $, the axis of symmetry is $ x = -\frac{6}{2} = -3 $.

To graph the function, plot points or use a graphing tool, keeping in mind that it's a parabola opening upwards since the coefficient of $ x^2 $ is positive.

To find the maximum or minimum value, since the coefficient of $ x^2 $ is positive, the parabola opens upwards, and there is a minimum value. To find it, substitute the $ x $-coordinate of the axis of symmetry into the original function to find the corresponding $ y $-coordinate. So, substitute $ x = -3 $ into $ y = (-3)^2 + 6(-3) + 2 $ to find the minimum value.