The equivalent equation is option (D) [tex]y=(x-6)^{2}-2[/tex].
A quadratic equation is a polynomial which has the highest degree equal to two. It is a second-degree equation of the form ax² + bx + c = 0, where a, b, are the coefficients, c is the constant term, and x is the variable.
For the given situation,
The equation is y-34=x(x-12)
⇒ [tex]y-34=x(x-12)[/tex]
⇒ [tex]y-34=x^{2} -12x[/tex]
⇒ [tex]y=x^{2} -12x+34[/tex]
⇒ [tex]y=x^{2} -12x+36-2[/tex]
⇒ [tex]y=(x-6)^{2}-2[/tex]
Hence we can conclude that the equivalent equation is option (D) y=(x-6)^{2}-2.
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