Factored Form:& a(x-p)(x-q)
Standard Form:& ax^2+bx+c
In the factored form p and q are the roots of the function. Since we are told the roots are x = - i and x = i, we can partially write the factored form of our function.
y = a( x-( - i ) ) ( x- i )
⇕
y = a( x+ i ) ( x-i )
Since a does not have any effect on the roots, we can choose any value. For simplicity, we will let a=1.
y = 1( x+ i ) ( x-i )
Finally, let's use the Distributive Property and Difference of Squares to obtain the standard form.
Please note that this is just one example of a quadratic function that satisfies the given requirements.
b We can write a quadratic function in factored form using the two given roots. Then we will change it to standard form by multiplying the factors.
Factored Form:& a(x-p)(x-q)
Standard Form:& ax^2+bx+c
In the factored form, p and q are the roots of the function. Since we are told the roots are x = 1+sqrt(2) and x = 1-sqrt(2), we can partially write the factored form of our function.
y = a ( x - ( 1 + sqrt(2) ) ) ( x - ( 1 - sqrt(2)) )
⇕
y = a( x-1-sqrt(2) ) ( x-1+sqrt(2) )
Since a does not have any effect on the roots, we can choose any value. For simplicity, we will let a=1.
y = 1( x-1-sqrt(2) ) ( x-1+sqrt(2) )
Finally, let's use the Distributive Property to obtain the standard form.
