Zero points of a function are its intersection points with the $X$-axis.

To find them, we set $Y=0$,

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 $X$-axis.

To find them, we set $Y=0$,

we get an equation that can sometimes be solved using a trinomial or the quadratic formula.

**Two results -**

In this case, the function intersects the $X$-axis at two different points.**One result -**

In this case, the function intersects the $X$-axis at only one point, meaning the vertex of the parabola is exactly on the $X$-axis.**No results -**

In this case, the function does not intersect the $X$-axis at all, meaning it hovers above or below it.

Determine the points of intersection of the function

\( y=(x-3)(x+3) \)

With the X

**Zero points describe a situation where the function equals zero.**

Let's look at an example:

We have the function

$X^2-4x+5$

We substitute into the quadratic formula and get:

${-4 \pm \sqrt{(-4)^2-4*1*5} \over 21}=-\frac{4\pm\sqrt{-4}}{2}$

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.

Test your knowledge

Question 1

Determine the points of intersection of the function

\( y=(x-5)(x+5) \)

With the X

Question 2

Determine the points of intersection of the function

\( y=x(x+5) \)

With the X

Question 3

Determine the points of intersection of the function

\( y=(x+7)(x+2) \)

With the X

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
- 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)