How do you find the axis of symmetry and vertex point of the function: #y= -4x^2+24x+6#?

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Answer 1 · 2018-04-05T09:30:10

Axis of symmetry formula

While there are several ways to find the axis of symmetry, the simplest method here is probably to just the formula,

#x=(-b)/(2a)#

Where we get the #b# and #a# values from the general formula,

#y = ax^2 + bx + c#

Substituting your formula into the equation, we can see that:
#a = -4#
#b=24#

So, to determine the axis of symmetry:

#x=(-b)/(2a)#

#x=(-(24))/(2(-4))#

#x=3#

The axis of symmetry is the x value of the vertex point. Knowing this, we simply substitute #x = 3# in your equation:

y = #-4x^2 + 24x + 6#

y = #-4(3)^2 + 24(3) + 6#

y = #42#

So, the vertex point will be at #3, 42#.