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-5)
B
bExample solution: y=(x+6)(x-6)
C
cExample solution: y=(x+0.25)(x-0.75)
Practice makes perfect
a We want to write a 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 (5,0). Thus, the x-intercepts are 0 and 5.
To write the equation of a parabola with x-intercepts 0 and 5, 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- 5)
⇕
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-5)
⇕
y=x(x-5)
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 (- 6, 0) and (6,0). Thus, the x-intercepts are - 6 and 6.
To write the equation of the parabola with x-intercepts - 6 and 6, 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-(- 6))(x- 6)
⇕
y=a(x+6)(x-6)
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+6)(x-6)
⇕
y=(x+6)(x-6)
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 (- 0.25, 0) and (0.75,0). Thus, the x-intercepts are - 0.25 and 0.75.
To write the equation of the parabola with x-intercepts - 0.25 and 0.75, 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-(- 0.25))(x- 0.75)
⇕
y=a(x+0.25)(x+0.75)
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+0.25)(x-0.75)
⇕
y=(x+0.25)(x-0.75)
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.
