Question

identifying the vertex
the vertex form of a quadratic function is ( f(x) = a(x - h)^2 + k ). what is the vertex of each function? match the function rule with the coordinates of its vertex.
( f(x) = 6(x + 9)^2 - 5 )
( f(x) = 5(x - 6)^2 + 9 )
( f(x) = 9(x - 5)^2 - 9 )
( f(x) = 8(x - 5)^2 + 6 )
( f(x) = 9(x + 5)^2 - 6 )
( (-9, -5) )
( (6, 9) )
( (5, 6) )
( (-5, -6) )
( (5, -9) )

Explanation:

Step1: Recall vertex form rule

For $f(x)=a(x-h)^2+k$, vertex is $(h,k)$.

Step2: Match first function

$f(x)=6(x+9)^2-5 = 6(x-(-9))^2-5$, so vertex $(-9,-5)$.

Step3: Match second function

$f(x)=5(x-6)^2+9$, so vertex $(6,9)$.

Step4: Match third function

$f(x)=6(x-5)^2-9$, so vertex $(5,-9)$.

Step5: Match fourth function

$f(x)=9(x-5)^2+6$, so vertex $(5,6)$.

Step6: Match fifth function

$f(x)=9(x+5)^2-6 = 9(x-(-5))^2-6$, so vertex $(-5,-6)$.

Answer:

• $f(x)=6(x+9)^2-5$ matches $(-9,-5)$
• $f(x)=5(x-6)^2+9$ matches $(6,9)$
• $f(x)=6(x-5)^2-9$ matches $(5,-9)$
• $f(x)=9(x-5)^2+6$ matches $(5,6)$
• $f(x)=9(x+5)^2-6$ matches $(-5,-6)$