identifying quadratic functions in factored form\na. $f(x)=x^{2}-11x - 12$\nb. $f(x)=x^{2}-4x - 12$\nc…

identifying quadratic functions in factored form\na. $f(x)=x^{2}-11x - 12$\nb. $f(x)=x^{2}-4x - 12$\nc. $f(x)=x^{2}+x - 12$\nd. $f(x)=x^{2}-x - 12$\nmatch each quadratic function given in factored form with its equivalent standard form listed on the left.\n$f(x)=(x + 2)(x - 6)$\n$f(x)=(x - 4)(x + 3)$\n$f(x)=(x - 12)(x + 1)$\n$f(x)=(x - 3)(x + 4)$

identifying quadratic functions in factored form\na. $f(x)=x^{2}-11x - 12$\nb. $f(x)=x^{2}-4x - 12$\nc. $f(x)=x^{2}+x - 12$\nd. $f(x)=x^{2}-x - 12$\nmatch each quadratic function given in factored form with its equivalent standard form listed on the left.\n$f(x)=(x + 2)(x - 6)$\n$f(x)=(x - 4)(x + 3)$\n$f(x)=(x - 12)(x + 1)$\n$f(x)=(x - 3)(x + 4)$

Answer

Explanation:

Step1: Expand ((x + 2)(x - 6))

Using FOIL method: (x\times x+x\times(-6)+2\times x + 2\times(-6)=x^{2}-6x + 2x-12=x^{2}-4x - 12), so ((x + 2)(x - 6)) matches B.

Step2: Expand ((x - 4)(x + 3))

Using FOIL method: (x\times x+x\times3+(-4)\times x+(-4)\times3=x^{2}+3x-4x - 12=x^{2}-x - 12), so ((x - 4)(x + 3)) matches D.

Step3: Expand ((x - 12)(x + 1))

Using FOIL method: (x\times x+x\times1+(-12)\times x+(-12)\times1=x^{2}+x-12x - 12=x^{2}-11x - 12), so ((x - 12)(x + 1)) matches A.

Step4: Expand ((x - 3)(x + 4))

Using FOIL method: (x\times x+x\times4+(-3)\times x+(-3)\times4=x^{2}+4x-3x - 12=x^{2}+x - 12), so ((x - 3)(x + 4)) matches C.

Answer:

(f(x)=(x + 2)(x - 6)) matches B. (f(x)=x^{2}-4x - 12) (f(x)=(x - 4)(x + 3)) matches D. (f(x)=x^{2}-x - 12) (f(x)=(x - 12)(x + 1)) matches A. (f(x)=x^{2}-11x - 12) (f(x)=(x - 3)(x + 4)) matches C. (f(x)=x^{2}+x - 12)