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What is the vertex form of #y=x^2-4x-12 #?

Answer 1

Isaiah Anthony

# y = (x-2)^2 - 16#

The standard form of a quadratic function is # y = ax^2+bx+c#

the equation here # y = x^2-4x-12 color(black)(" is of this form ")#

For instance, a = 1, b = -4, and c = -12

The quadratic function's vertex form is

# y = a(x-h)^2 + k # where (h , k ) are the coords of the vertex.

the x-coord of the vertex = #-b/(2a) = -(-4)/2 = 2 # substitute x = 2 into original function for y-coord.

y = #(2)^2 - 4(2) -12 = 4 - 8 - 12 = -16# hence (h , k )= (2 , -16 ) and a = 1

# rArr y = (x - 2 )^2 - 16# graph{x^2-4x-12 [-40, 40, -20, 20]}

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Answer from HIX Tutor

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