Factored Form:& y=a(x-p)(x-q)
Standard Form:& y=ax^2+bx+c
In the factored form p and q are the roots of the equation. Let's substitute 34 and -2 to partially write our equation.
y=a(x- 3/4 )( x-(-2))
⇕
y=a( x- 3/4 )(x+2)
Since a does not have any effect on the roots, we can choose any value other than 0. In order to have integer coefficients, we will let a= 4. This will allow us to eliminate the fraction after we distribute.
y= 4( x- 3/4 )(x+2)
Finally, let's use the Distributive Property to obtain the standard form.
Please note that this is just one example of a quadratic equation that satisfies the given requirements.
b Similarly as in Part A, we will first write the equation in factored form and then multiply the factors to obtain the standard form. Since we are told the x-intercepts are -sqrt(5) and sqrt(5), we can partially write the factored form of our equation.
y=a( x-( - sqrt(5)) ) ( x-sqrt(5) )
⇕
y=a( x+ sqrt(5) ) ( x-sqrt(5) )We can choose any value of a except 0. For simplicity, we will let a= 1.
y= 1( x+ sqrt(5) ) ( x-sqrt(5) )
⇕
y=( x+ sqrt(5) ) ( x-sqrt(5) )
Finally, let's use the Distributive Property to obtain the standard form. Note that it is a product of conjugate binomials.
