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 - 5 and 8, we can partially write the factored form of our equation.
a(x-( - 5))(x-8)=0
⇕
a(x+5)(x-8)=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=1.
1(x+5)(x-8)=0
⇕
(x+5)(x-8)=0
Finally, let's use the Distributive Property 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 equation in factored form using the given roots. Then we will change it to standard form by multiplying the factors.
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 3 and - 2, we can partially write the factored form of our equation.
a(x-3)(x-(- 2))=0
⇕
a(x-3)(x+2)=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=1.
1(x-3)(x+2)=0
⇕
(x-3)(x+2)=0
Finally, let's use the Distributive Property to obtain the standard form.
Please note that this is just one example of a quadratic function that satisfies the given requirements.
c We can write a quadratic equation in factored form using the given roots. Then we will change it to standard form by multiplying the factors.
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 12 and - 10, we can partially write the factored form of our equation.
a(x-1/2)(x-(- 10))=0
⇕
a(x-1/2)(x+10)=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=2. This will allow us to eliminate the fractions when we distribute.
2(x-1/2)(x+10)=0
Finally, let's use the Distributive Property to obtain the standard form.
Please note that this is just one example of a quadratic function that satisfies the given requirements.
d We can write a quadratic equation in factored form using the given roots. Then we will change it to standard form by multiplying the factors.
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 23 and - 57, we can partially write the factored form of our equation.
a( x-2/3 )( x-( - 5/7 ) )=0
⇕
a( x- 2/3 ) ( x+5/7 )=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=21. This is a common multiple of both denominators of the given roots and will allow us to eliminate the fractions when we distribute.
21( x- 2/3 ) ( x+5/7 )=0
Finally, let's use the Distributive Property to obtain the standard form.
