Exercise 14 Page 255

We can write a quadratic equation in factored form using the given roots. Then we will rewrite it in standard form by multiplying the factors. cc Factored Form:& a(x-p)(x-q)=0 Standard Form:& ax^2+bx+c=0 In the factored form, p and q are the roots of the equation. Since we are told the roots are - 6 and 14, we can partially write the factored form of our equation. a( x-( - 6 ) ) ( x-1/4 )=0 ⇕ a( x+ 6 ) ( x-1/4 )=0 Since a does not have any effect on the roots, we can choose any value. For simplicity and in order to have integer coefficients, we will let a=4. This will allow us to eliminate the fractional part when we distribute. 4( x+ 6) ( x-1/4 )=0 Finally, let's use the Distributive Property to write the standard form.

Please note that this is just one example of a quadratic function that satisfies the given requirements. There are infinite possible solutions.