Question

Question 9(Multiple Choice Worth 1 points)

(08.07 LC)
The quadratic function f(x) has roots of -4 and 3 and point (2,-6) lies on f(x). What is the equation of f(x)?
Of(x) = (x+3)(x-4)
Of(x)=(x-3)(x+4)
Of(x)=3(x+3)(x-4)
Of(x)=3(x-3)(x+4)
Question 10g

Answer 1

`\begin{cases} x = -4 &\implies x +4=0\\ x = 3 &\implies x -3=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +4 )( x -3 ) = \stackrel{0}{f(x)}} \hspace{5em}\textit{we also know that } \begin{cases} x ~~ ~~ = ~~ 2\\ f(x)=-6 \end{cases} \\\\\\ a ( 2 +4 )( 2 -3 ) = -6\implies a(6)(-1)=-6\implies -6a=-6 \\\\\\ a=\cfrac{-6}{-6}\implies a=1 \\\\[-0.35em] ~\dotfill\\\\ 1( x +4 )( x -3 ) =f(x)\implies {\Large \begin{array}{llll} ( x +4 )( x -3 ) =f(x) \end{array}}`