Chapter 1.3, Problem 63E

Solution

To write: A quadratic function with zeros that are equidistant from $10$ on the number line.

A quadratic function with zeros that are equidistant from $10$ on the number line is $x^2-20x+84=0$ .

Given information:

Zeros of a quadratic function are equidistant from $10$ on the number line.

Calculation:

Let the two numbers be $6$ and $14$ . Thus, $x=6$ and $x=14$ .

The roots of an equation $x^2+bx+c=0$ are the $x$ -values of that equation that make the equation zero. Zeros of $y=a\left(x-p\right)\left(x-q\right)$ are $p$ and $q$ as the function's value is zero when $x=p$ and $x=q$ . Thus, $\left(x-6\right)\left(x-14\right)=0$ . This can be expanded as $x^2-20x+84=0$

A possible equation is $x^2-20x+84=0$