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.
Finding the Zeros of a Parabola
Finding the zeros of a quadratic function of the form \(y=ax^2+bx+c\)
When trying to find the zero point, you can encounter three possible results:
- Two results -
In this case, the function intersects the -axis at two different points. - One result -
In this case, the function intersects the -axis at only one point, meaning the vertex of the parabola is exactly on the -axis. - No results -
In this case, the function does not intersect the -axis at all, meaning it hovers above or below it.
Test yourself on finding zero points!
Determine the points of intersection of the function
\( y=(x-2)(x+3) \)
With the X
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.
Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today
Test your knowledge
Question 1
Determine the points of intersection of the function
\( y=(x-1)(x+10) \)
With the X
Question 2
Determine the points of intersection of the function
\( y=(x-3)(x+3) \)
With the X
Question 3
Determine the points of intersection of the function
\( y=(x-5)(x+5) \)
With the X
examples with solutions for finding zero points
Exercise #1
Determine the points of intersection of the function
With the X
Video Solution
Step-by-Step Solution
To find the point of intersection with the X-axis, we will want 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 will check the possibilities.
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!
Answer
Exercise #2
Determine the points of intersection of the function
With the X
Video Solution
Answer
Exercise #3
Determine the points of intersection of the function
With the X
Video Solution
Answer
Exercise #4
Determine the points of intersection of the function
With the X
Video Solution
Answer
Exercise #5
Determine the points of intersection of the function
With the X
Video Solution
Answer
Related Subjects
- Quadratice Equations and Systems of Quadraric Equations
- Quadratic Equations System - Algebraic and Graphical Solution
- Solution of a system of equations - one of them is linear and the other quadratic
- Intersection between two parabolas
- Word Problems
- Properties of the roots of quadratic equations - Vieta's formulas
- Ways to represent a quadratic function
- Various Forms of the Quadratic Function
- Standard Form of the Quadratic Function
- Vertex form of the quadratic equation
- Factored form of the quadratic function
- The quadratic function
- Quadratic Inequality
- Parabola
- Symmetry in a parabola
- Plotting the Quadratic Function Using Parameters a, b and c
- Methods for solving a quadratic function
- Completing the square in a quadratic equation
- Squared Trinomial
- The quadratic equation
- Families of Parabolas
- The functions y=x²
- Family of Parabolas y=x²+c: Vertical Shift
- Family of Parabolas y=(x-p)²
- Family of Parabolas y=(x-p)²+k (combination of horizontal and vertical shifts)
