Determine the vertex, the equation of the axis of symmetry, and the maximum or minmum value of the function. f(x)=(x-6)(x+4)Explain   Thanks

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samhouston | Middle School Teacher | (Level 1) Associate Educator

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Use FOIL to multiply (x-6)(x+4)

x^2 - 6x + 4x - 24

x^2 - 2x - 24

In standard form:

y = x^2 + (-2x) + (-24)

a = 1, b = -2, c = -24

The vertex is (x,y) where x = -b/2a

x = 2/2*1 = 1

Substitute 1 in for x in the equation to find y

y = 1^2 + (-2*1) + (-24)

y = 1 + (-2) + (-24)

y = -25

Vertex:  (1, -25)

Since the parabola opens up, this point is the minimum.

The equation for the axis of symmetry is x = 1

Graph:

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