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To find the intersection points between the two given parabolas, we need to solve the equation:

\[ f(x) = h(x) \]

The equations are:

\[
f(x) = x^2 - 2x - 3
\]
\[
h(x) = -x^2 + 4x - 3
\]

Setting \( f(x) = h(x) \):

\[
x^2 - 2x - 3 = -x^2 + 4x - 3
\]

Combine like terms:

\[
x^2 + x^2 - 2x - 4x - 3 + 3 = 0
\]

\[
2x^2 - 6x = 0
\]

Factorize:

\[
2x(x - 3) = 0
\]

Solve for \(x\):

\[
x = 0 \quad \text{or} \quad x = 3
\]

Substitute \(x = 0\) into one of the original equations, say \(f(x)\):

\[
f(0) = 0^2 - 2(0) - 3 = -3
\]

Thus, one intersection point is \((0, -3)\).

Substitute \(x = 3\) into \(f(x)\):

\[
f(3) = 3^2 - 2(3) - 3 = 9 - 6 - 3 = 0
\]

Thus, another intersection point is \((3, 0)\).

### Conclusion:

The intersection points are:

\[
(0, -3) \quad \text{and} \quad (3, 0)
\]

Would you like further clarification or visual representation? Here are 5 related questions for exploration:

1. How do the shapes of the parabolas determine the nature of their intersections?
2. What happens if the two parabolas have no intersections?
3. How can the discriminant of a quadratic equation help in such problems?
4. How can this be solved graphically instead of algebraically?
5. What is the geometric significance of solving \( f(x) = h(x) \)?

**Tip**: Always factorize carefully to avoid missing solutions!

Bepaal de snijpunten (als die er zijn) tussen de volgende parabolen: f(x) = x^2 - 2x - 3 en h(x) = -x^2 + 4x - 3.

Discover how to determine the intersection points of two parabolas: f(x) = x^2 - 2x - 3 and h(x) = -x^2 + 4x - 3. This problem demonstrates solving quadratic equations algebraically, factoring, and finding the roots. Ideal for Grades 9-10.

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