the graph of ( y = x^{2}+11x + 24 ) is equivalent to the graph of which equation?\n( y=(x + 8)(x + 3) )\n(…

Explanation:

Step1: Expand (y=(x + 8)(x + 3))

Use the FOIL method: ((a + b)(c + d)=ac+ad+bc+bd). For (y=(x + 8)(x + 3)), we have (y=x\times x+x\times3+8\times x + 8\times3). Simplify: (y=x^{2}+3x+8x + 24=x^{2}+11x+24).

Step2: Expand (y=(x + 4)(x + 6))

Using FOIL: (y=x\times x+x\times6+4\times x+4\times6). Simplify: (y=x^{2}+6x+4x + 24=x^{2}+10x+24).

Step3: Expand (y=(x + 9)(x + 2))

Using FOIL: (y=x\times x+x\times2+9\times x+9\times2). Simplify: (y=x^{2}+2x+9x + 18=x^{2}+11x+18).

Step4: Expand (y=(x + 7)(x + 4))

Using FOIL: (y=x\times x+x\times4+7\times x+7\times4). Simplify: (y=x^{2}+4x+7x + 28=x^{2}+11x+28).

Answer:

(y=(x + 8)(x + 3))