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# Interpreting Quadratic Functions in Vertex Form

## Interpreting Quadratic Functions in Vertex Form 1.9 - Solution

We want to identify the vertex and the axis of symmetry of the graph of given quadratic function. Note that the function is already expressed in vertex form where $a,$ $h,$ and $k$ are either positive or negative numbers. $\begin{gathered} y=3\big(x-2\big)^2+5 \end{gathered}$ It is important to note that we do not need to graph the parabola to identify the desired information. Let's compare the general formula for the vertex form with our equation. \begin{aligned} \textbf{General formula: }y=&\ {\color{#FF0000}{a}}(x-{\color{#0000FF}{h}})^2 +\textcolor{magenta}{k} \\ \textbf{Equation: }y=&\ {\color{#FF0000}{3}}\big(x-{\color{#0000FF}{2}}\big)^2+\textcolor{magenta}{5} \end{aligned} We can see that ${\color{#FF0000}{a}}={\color{#FF0000}{3}},$ ${\color{#0000FF}{h}}={\color{#0000FF}{2}},$ and $\textcolor{magenta}{k}=\textcolor{magenta}{5}.$

### Vertex

The vertex of a quadratic function written in vertex form is the point $({\color{#0000FF}{h}},\textcolor{magenta}{k}).$ For this exercise, we have ${\color{#0000FF}{h}}={\color{#0000FF}{2}}$ and $\textcolor{magenta}{k}=\textcolor{magenta}{5}.$ Therefore, the vertex of the given equation is $({\color{#0000FF}{2}},\textcolor{magenta}{5}).$

### Axis of Symmetry

The axis of symmetry of a quadratic function written in vertex form is the vertical line with equation $x={\color{#0000FF}{h}}.$ As we have already noticed, for our function, this is ${\color{#0000FF}{h}}={\color{#0000FF}{2}}.$ Thus, the axis of symmetry is the line $x={\color{#0000FF}{2}}.$