<span>f<span>(x)</span></span>=<span><span>(x+4)</span>2</span>−<span>13
</span>
Converting to Vertex Form
1. Start by placing brackets around the first two terms.
<span><span><span>f<span>(x)</span></span>=<span>x2</span>+8x+3</span><span><span>f<span>(x)</span></span>=<span>(<span>x2</span>+8x)</span>+3</span></span>
2. In order to make the bracketed terms a perfect square trinomial, we must add a "c" term as in <span>a<span>x2</span>+bx+c</span>. Since c, in a perfect square trinomial is denoted by the formula <span>c=<span><span>(<span>b2</span>)</span>2</span></span>, take the value of b to find the value of c.
<span><span>f<span>(x)</span></span>=<span>(<span>x2</span>+8x+<span><span>(<span>82</span>)</span>2</span>)</span>+3</span>
3. However, adding <span><span>(<span>82</span>)</span>2</span> would change the value of the equation. Thus, subtract <span><span>(<span>82</span>)</span>2</span> from the <span><span>(<span>82</span>)</span>2</span> you just added.
<span><span>f<span>(x)</span></span>=<span>(<span>x2</span>+8x+<span><span>(<span>82</span>)</span>2</span>−<span><span>(<span>82</span>)</span>2</span>)</span>+3</span>
4. Multiply <span>(−<span><span>(<span>82</span>)</span>2</span>)</span> by the a term as in <span>a<span>x2</span>+bx+c</span> to bring it outside the brackets.
<span><span>f<span>(x)</span></span>=<span>(1<span>x2</span>+8x+<span><span>(<span>82</span>)</span>2</span>)</span>+3−<span>(<span><span>(<span>82</span>)</span>2</span>×1)</span></span>
5. Simplify.
<span><span><span>f<span>(x)</span></span>=<span>(<span>x2</span>+8x+16)</span>+3−16</span><span><span>f<span>(x)</span></span>=<span>(<span>x2</span>+8x+16)</span>−13</span></span>
6. Lastly, factor the perfect square trinomial.
<span><span><span><span><span>f<span>(x)</span></span>=<span><span>(x+4)</span>2(squared)</span>−13</span></span></span></span>