Question

Consider the given quadratic equations. Equation A Equation B Equation C Equation D y = 3x2 − 6x + 21 y = 3x2 − 6x + 18 y = 3(x − 1)2 + 18 y = 3(x − 1)2 + 21 Complete the following statement. Equations are equivalent, and of those, equation is in the form most useful for identifying the extreme value of the function it defines.

Answer 1

Answer:

  Equations A and C are equivalent, and of those, equation C is in the form most useful ...

Step-by-step explanation:

In standard form, the equations are ...

Equation A: y = 3x² -6x +21

Equation B: y = 3x² -6x +18

Equation C: y = 3x² -6x +21 . . . . equivalent to A

Equation D: y = 3x² -6x +24

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Equation C is in vertex form, so the vertex (extreme value) can be read directly from the equation. It is (x, y) = (1, 18).

Equations A and C are equivalent; equation C is most useful for finding the vertex.

Answer 2

Answer with explanation:

→→Two equations or two polynomials are said to be equivalent, if written in distinct ways, and real value of variables is substituted in both equivalent and Original Polynomial, the numerical value of both the polynomials are Same.

→→The four Quadratic Polynomials are:

$1.\text{Equation} A: y = 3x^2 - 6 x + 21\\\\2.\text{Equation} B: y = 3x^2 - 6 x + 18\\\\3.\text{Equation} C: y = 3(x-1)^2 +18=3(x^2-2 x +1)+18\\\\y=3x^2 - 6 x +18+3\\\\y=3x^2 - 6 x +21\\\\3.\text{Equation} C: y = 3(x-1)^2 +21$

→→If you will look at Equation A and Equation C, both the equation are Quadratic, Coefficient of x², Coefficient of x, as well as , constant term is same in both the equation.So, Equation A, and Equation C, are equivalent.

→→If you will look at the function,

$y=3\times (x-1)^2+18\\\\y-18=3\times(x-1)^2$

at, x=1, y=18, which is extreme value of the function, as at vertex of the parabola , Parabola attains it's Maximum value.

⇒⇒Equations A and C,

[$1.\text{Equation} A: y = 3x^2 - 6 x + 21\\\\3.\text{Equation} C: y = 3(x-1)^2 +18$]

are equivalent, and of those, equation is in the form most useful for identifying the extreme value is $3.\text{Equation} C: y = 3(x-1)^2 +18$]  function it defines.