Question

Consider the function shown on the graph.4512-299+6-3-¹3--6-9--12-15(8, 15)(3, 0)(7,0)1 2 3 4 5 6 7 8 9XWhich function does the graph represent?O f(x) = (x+3)(x + 7Of(x) = (x-3)(x-7)Of(x)= 3(x-3)(x-7)O f(x)= 11(x+3)(x + 7)

Answer 1

`f(x)=3(x-3)(x-7)`

Step-by-step explanation

The intercept form of a quadratic equation is

`\begin{gathered} y=a(x-p)(x-q) \\ where\text{ p and q are the roots of the function} \end{gathered}`

so

Step 1

find p and q values

`\begin{gathered} p\text{ is the value for x where the function becomes zero, so check the graph} \\ (3,0) \\ so\text{ p=3} \\ and\text{ q} \\ (7,0) \\ so \\ q=7 \end{gathered}`

p=3

q=7

Step 2

now, to find the a value we need another point of the graph

check the vertex , it is

`(5,-12)`

so, replace

`\begin{gathered} x=5 \\ y=-12 \\ y=a(x-p)(x-q) \\ replacing \\ -12=a(5-3)(5-7) \\ -12=a*2*-2 \\ -12=-4a \\ divide\text{ both sides by -4} \\ (-12)/(-4)=(-4a)/(-4) \\ 3=a \end{gathered}`

so

a=3

therefore, replacing in the formula we have the answer

`f(x)=3(x-3)(x-7)`

I hope this helps you