In factored form the equation can be written as y=a(x-b)(x-c). In this form, the equation's roots are b and c.
B
b
In factored form the equation can be written as y=a(x-b)(x-c). In this form, the equation's roots are b and c.
C
c
In factored form the equation can be written as y=a(x-b)(x-c)(x-d). In this form, the equation's roots are b, c, and d.
D
d
In factored form the equation can be written as y=a(x-b)(x-c)(x-d). In this form, the equation's roots are b, c, and d.
A
a
Example Solution: y=x^2+6x+10
B
b
Example Solution: y=x^2-10x+16
C
c
Example Solution: y=x^3+2x^2-7x-14
D
d
Example Solution: y=x^3+2x^2-14x-40
Practice makes perfect
a
The function has two roots, which means we can write the expression as a second degree function in factored form.
y=a(x-b)(x-c)
In this equation, b and c are the equation's roots and a is the stretch factor, which we will assume is 1. From the exercise, we know that the roots are a=-3+i and b=3-i. Let's substitute the equation's roots in our equation and simplify the right-hand side.
Like in Part A, we have two roots, which means the function we are looking for is a second degree function. This means we can write it in factored form.
y=a(x-b)(x-c)
Let's substitute our roots into this equation and simplify. We will assume a stretch factor of a=1.
In this case we have three solutions, which means we can write the function in the following way.
y=a(x-b)(x-c)(x-d)
In this form, b, c, and d are our roots. By substituting these into the equation, we can determine the function. Again, we will assume a stretch factor of a=1.
Like in Part C, we have three roots, which means we can write the equation in factored form in the following way.
y=a(x-b)(x-c)(x-d)
In this form, b, c, and d are our roots. By substituting these into the equation, we can determine the function. We will assume a stretch factor of 1.
