Zero points of a function are its intersection points with the -axis.
To find them, we set ,
we get an equation that can sometimes be solved using a trinomial or the quadratic formula.
Zero points of a function are its intersection points with the -axis.
To find them, we set ,
we get an equation that can sometimes be solved using a trinomial or the quadratic formula.
The following function has been graphed below:
\( f(x)=-x^2+5x+6 \)
Calculate points A and B.
Zero points describe a situation where the function equals zero.
Let's look at an example:
We have the function
We substitute into the quadratic formula and get:
This equation has no solution because the delta inside the root is negative. Therefore, this equation never equals zero, it hovers above the X-axis, and it has no zero points.
The following function has been graphed below:
\( f(x)=x^2-6x+5 \)
Calculate points A and B.
\( \)
The following function has been graphed below:
\( f(x)=x^2-8x+16 \)
Calculate point A.
The following function has been graphed below:
\( f(x)=x^2-8x+16 \)
Calculate point C.
Determine the points of intersection of the function
With the X
In order to find the point of the intersection with the X-axis, we first need to establish that Y=0.
0 = (x-5)(x+5)
When we have an equation of this type, we know that one of these parentheses must be equal to 0, so we begin by checking the possible options.
x-5 = 0
x = 5
x+5 = 0
x = -5
That is, we have two points of intersection with the x-axis, when we discover their x points, and the y point is already known to us (0, as we placed it):
(5,0)(-5,0)
This is the solution!
The following function has been graphed below:
Calculate points A and B.
The following function has been graphed below:
Calculate points A and B.
The following function has been graphed below:
Calculate point A.
The following function has been graphed below:
Calculate point C.