b Use the factored form of the equation of a parabola, y=a(x+b)(x+c).
C
c Use the factored form of the equation of a parabola, y=a(x+b)(x+c).
A
aExample Solution: y=x(x-4)
B
bExample Solution: y=(x+2)(x-2)
C
cExample Solution: y=(x+1/2)(x-3/2)
Practice makes perfect
a We want to write the possible equation of the given parabola. Let's look at the given graph!
As we can see, the graph crosses the x-axis at the points (0, 0) and (4,0). Thus, the x-intercepts are 0 and 4.
To write the equation of the parabola with x-intercepts 0 and 4, we will use the factored form of a quadratic function.
y=a(x+b)(x+c)
⇕
y=a(x-(- b))(x-( - c))
In this form - b and - c are the intercepts. With this information, we can partially write our equation.
y=a(x- )(x- 4)
⇕
y=ax(x-4)
Since a does not have any effect on the x-intercepts, we can choose any value. For simplicity we will let a=1.
y=1x(x-4)
⇕
y=x(x-4)
We found a possible equation for the given parabola. Please note that this is just one example of a quadratic function that has the given x-intercepts.
b We want to write the possible equation of the given parabola. Let's look at the given graph!
As we can see, the graph crosses the x-axis at the points (- 2, 0) and (2,0). Thus, the x-intercepts are - 2 and 2.
To write the equation of the parabola with x-intercepts - 2 and 2, we will use the factored form of a quadratic function.
y=a(x+b)(x+c)
⇕
y=a(x-(- b))(x-( - c))
In this form - b and - c are the intercepts. With this information, we can partially write our equation.
y=a(x-(- 2))(x- 2)
⇕
y=a(x+2)(x-2)
Since a does not have any effect on the x-intercepts, we can choose any value. For simplicity we will let a=1.
y=1(x+2)(x-2)
⇕
y=(x+2)(x-2)
We found a possible equation for the given parabola. Please note that this is just one example of a quadratic function that has the given x-intercepts.
c We want to write the possible equation of the given parabola. Let's look at the given graph!
As we can see, the graph crosses the x-axis at the points (- 12, 0) and ( 32,0). Thus, the x-intercepts are - 12 and 32.
To write the equation of the parabola with x-intercepts - 12 and 32, we will use the factored form of a quadratic function.
y=a(x+b)(x+c)
⇕
y=a(x-(- b))(x-( - c))
In this form, - b and - c are the intercepts. With this information, we can partially write our equation.
y=a(x-(- 1/2))(x- 3/2)
⇕
y=a(x+1/2)(x-3/2)
Since a does not have any effect on the x-intercepts, we can choose any value. For simplicity we will let a=1.
y=1(x+1/2)(x-3/2)
⇕
y=(x+1/2)(x-3/2)
We found a possible equation for the given parabola. Please note that this is just one example of a quadratic function that has the given x-intercepts.
