Write $$ g(x)=-16 x+x^{2} $$ in vertex form. $$ \begin{array}{ll} ext { 1. Write the function in standard form. } & g(x)=x^{2}-16 x \ ext { 2. Form a perfect square trinomial by adding and } & b=-16 ext {, so }\left(\frac{-16}{2} ight)^{2}=64 \ ext { subtracting }\left(\frac{b}{2} ight)^{2} & g(x)=\left(x^{2}-16 x+64 ight)-64 \ ext { 3. Write the trinomial as a binomial squared. } & g(x)=(x-\square \ ext { 4. Write the function is in vertex form, if needed. }\end{array} $$

Question

Write $$ g(x)=-16 x+x^{2} $$ in vertex form. $$ \begin{array}{ll}	ext { 1. Write the function in standard form. } & g(x)=x^{2}-16 x \ 	ext { 2. Form a perfect square trinomial by adding and } & b=-16 	ext {, so }\left(\frac{-16}{2}ight)^{2}=64 \ 	ext { subtracting }\left(\frac{b}{2}ight)^{2} & g(x)=\left(x^{2}-16 x+64ight)-64 \ 	ext { 3. Write the trinomial as a binomial squared. } & g(x)=(x-\square \ 	ext { 4. Write the function is in vertex form, if needed. }\end{array} $$

UpStudy AI · Accepted Answer

To write the function $$ g(x) = -16x + x^2 $$ in vertex form, we will follow the steps outlined in your problem. Let's go through each step carefully.

### Step 1: Write the function in standard form
The function is already given in standard form as:
$$
g(x) = x^2 - 16x
$$

### Step 2: Form a perfect square trinomial
To form a perfect square trinomial, we need to add and subtract $$\left(\frac{b}{2}\right)^2$$, where $$b = -16$$.

Calculating $$\left(\frac{-16}{2}\right)^2$$:
$$
\left(\frac{-16}{2}\right)^2 = (-8)^2 = 64
$$

Now, we can add and subtract 64 in the function:
$$
g(x) = (x^2 - 16x + 64) - 64
$$

### Step 3: Write the trinomial as a binomial squared
The trinomial $$x^2 - 16x + 64$$ can be factored as:
$$
g(x) = (x - 8)^2 - 64
$$

### Step 4: Write the function in vertex form
The vertex form of a quadratic function is given by:
$$
g(x) = a(x - h)^2 + k
$$
where $$(h, k)$$ is the vertex of the parabola.

From our expression, we can see that:
- $$a = 1$$
- $$h = 8$$
- $$k = -64$$

Thus, the vertex form of the function is:
$$
g(x) = (x - 8)^2 - 64
$$

### Final Answer
The function $$ g(x) $$ in vertex form is:
$$
g(x) = (x - 8)^2 - 64
$$
The function $$ g(x) $$ in vertex form is $$ g(x) = (x - 8)^2 - 64 $$.

Write in vertex form.

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Solución

Step 1: Write the function in standard form

Step 2: Form a perfect square trinomial

Step 3: Write the trinomial as a binomial squared

Step 4: Write the function in vertex form

Final Answer

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