Question

#13, can you please try to give a detailed run-through on how to identify the variables, and do the problem step by step, I have trouble learning math.

Answer 1

Given the general expression of a quadratic function,

`f(x)=ax^2+bx_{}+c`

The given function is,

`f(x)=(x-3)(x+8)`

Expanding the right-hand side of the equation

`(x-3)(x+8)`

Apply FOIL method:

`\begin{gathered} \mleft(a+b\mright)\mleft(c+d\mright)=ac+ad+bc+bd \\ \end{gathered}`

Therefore,

`\mleft(x-3\mright)\mleft(x+8\mright)=x* x+x*8-3* x-3*\: 8=x^2+8x-3x-24`

Simplify

`x^2+8x-3x-24=x^2+5x-24`

Therefore, the function in standard form is

`f(x)=x^2+5x-24`

Now, comparing the general quadratic function and the function given.

`\begin{gathered} ax^2=x^2 \\ (ax^2)/(x^2)=(x^2)/(x^2) \\ \therefore a=1 \end{gathered}`
`\begin{gathered} bx=5x \\ (bx)/(x)=(5x)/(x) \\ \therefore b=5 \end{gathered}`
`c=-24`

Hence, the answers are

`\begin{gathered} a=1 \\ b=5 \\ c=-24 \end{gathered}`