Finding the Zeros of a Parabola

🏆Practice finding zero points

Finding the zeros of a quadratic function of the form \(y=ax^2+bx+c\)

Zero points of a function are its intersection points with the XX-axis.
To find them, we set Y=0 Y=0 ,
we get an equation that can sometimes be solved using a trinomial or the quadratic formula.

When trying to find the zero point, you can encounter three possible results:

  1. Two results -
    In this case, the function intersects the XX-axis at two different points.
  2. One result -
    In this case, the function intersects the XX-axis at only one point, meaning the vertex of the parabola is exactly on the XX-axis.
  3. No results -
    In this case, the function does not intersect the XX-axis at all, meaning it hovers above or below it.
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Test yourself on finding zero points!

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Determine the points of intersection of the function

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

With the X

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Zero points describe a situation where the function equals zero.

Let's look at an example:
We have the function
X24x+5X^2-4x+5
We substitute into the quadratic formula and get:

4±(4)241521=4±42 {-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.

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