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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)

Consider the function shown on the graph45122996336912158 153 0701 2 3 4 5 6 7 8 9XWhich function does the graph representO fx x3x 7Ofx x3x7Ofx 3x3x7O fx 11x3x class=

Respuesta :

[tex]f(x)=3(x-3)(x-7)[/tex]

Explanation

The intercept form of a quadratic equation is

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

so

Step 1

find p and q values

[tex]\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}[/tex]

p=3

q=7

Step 2

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

check the vertex , it is

[tex](5,-12)[/tex]

so, replace

[tex]\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} \\ \frac{-12}{-4}=\frac{-4a}{-4} \\ 3=a \end{gathered}[/tex]

so

a=3

therefore, replacing in the formula we have the answer

[tex]f(x)=3(x-3)(x-7)[/tex]

I hope this helps you

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