\begin{tabular}{l} Write a quadratic function $$ f $$ whose zeros are -2 and 10 . \ $$ \qquad f(x)=\square $$ \ \hline$$ \square^{\square} $$ \ \hline$$ imes \infty $$ \ \hline\end{tabular}

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\begin{tabular}{l} Write a quadratic function $$ f $$ whose zeros are -2 and 10 . \ $$ \qquad f(x)=\square $$ \ \hline$$ \square^{\square} $$ \ \hline$$ 	imes \infty $$ \ \hline\end{tabular}

UpStudy AI · Accepted Answer

To write a quadratic function $$ f $$ whose zeros are -2 and 10, we can use the fact that if $$ r_1 $$ and $$ r_2 $$ are the roots (or zeros) of the quadratic function, then the function can be expressed in the form:

$$
f(x) = a(x - r_1)(x - r_2)
$$

where $$ a $$ is a non-zero constant. In this case, the roots are $$ r_1 = -2 $$ and $$ r_2 = 10 $$.

1. Substitute the roots into the equation:
   $$
   f(x) = a(x - (-2))(x - 10) = a(x + 2)(x - 10)
   $$

2. We can choose $$ a = 1 $$ for simplicity:
   $$
   f(x) = (x + 2)(x - 10)
   $$

3. Now, we will expand this expression:
   $$
   f(x) = x^2 - 10x + 2x - 20 = x^2 - 8x - 20
   $$

Thus, the quadratic function is:

$$
f(x) = x^2 - 8x - 20
$$

So, the final answer is:

$$
f(x) = x^2 - 8x - 20
$$
The quadratic function is $$ f(x) = x^2 - 8x - 20 $$.

Write a quadratic function whose zeros are -2 and 10 .

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