## Related questions with answers

Find the vertex and the axis of symmetry of the graph of the function. $f ( x ) = 5 ( x - 2 ) ^ { 2 }$

Solution

VerifiedWe would like to find the vertex and the axis of symmetry of the graph of the function

$\color{#4257b2}f(x)=5(x-2)^{2}$

First, we note that the function $\color{#4257b2}f(x)=5(x-2)^{2}$ is on the form $\color{#4257b2}f(x)=a(x-h)^{2}$ where $\color{#4257b2}a=5$ and $\color{#4257b2}h=2$, so we can use the characteristics of the function $\color{#4257b2}f(x)=a(x-h)^{2}$ to find the vertex and the axis of symmetry of the graph of $\color{#4257b2}f(x)$.

Since we know that in the function $\color{#4257b2}f(x)=a(x-h)^{2}$ the vertex is $\color{#4257b2}(h,\ 0)$, so the vertex of the graph of $\color{#4257b2}f(x)=5(x-2)^{2}$ is $\color{#c34632}(2,\ 0)$.

Also in the function $\color{#4257b2}f(x)=a(x-h)^{2}$ we know that the axis of symmetry is $\color{#4257b2}x=h$, so the axis of symmetry of the graph of $\color{#4257b2}f(x)=5(x-2)^{2}$ is $\color{#c34632}x=2$.

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