How do you find the axis of symmetry, and the maximum or minimum value of the function #y = 4x^2 + 5x – 1#?

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Answer 1 · 2018-06-22T14:17:54

#vertex: (-5/8, -91/16); " axis of symmetry": x = -5/8#
minimum

Given: #y = 4x^2 + 5x - 1#

When the equation is in standard form: #f(x) = Ax^2 + Bx + C#, you can find the vertex and the axis of symmetry as follows:

vertex: #(-B/(2A), f(-B/(2A)))#, axis of symmetry: #x = -B/(2A)#

#-B/(2A) = -5/(2*4) = -5/8#

#f(-5/8) = 4 (-5/8)^2 + 5(-5/8) - 1#

#= 4*(25/64) - 25/8 - 1#

#= 25/16 - 50/16 - 16/16 = -91/16#

#vertex: (-5/8, -91/16); " axis of symmetry": x = -5/8#

The vertex will be a minimum because #A# is positive.