To find the equation of the quadratic function graphed in the image, we can use key information from the graph.

Observations:

1. Vertex: The vertex of the parabola appears to be at $(-3, -4)$.
2. Form of Equation: Since this is a quadratic function, the equation can be written in vertex form: $y = a(x - h)^2 + k$ where $(h, k)$ is the vertex of the parabola. For this graph, $(h, k) = (-3, -4)$, so the equation becomes: $y = a(x + 3)^2 - 4$
3. Point on the Graph: To find the value of $a$, we can use another point on the graph. For example, the point $(-2, -3)$ lies on the graph.

Solving for $a$:

Substitute $(-2, -3)$ into the equation: $-3 = a(-2 + 3)^2 - 4$ Simplify: $-3 = a(1)^2 - 4$ $-3 = a - 4$ $a = 1$

Final Equation:

Thus, the equation of the parabola is: $y = (x + 3)^2 - 4$

Would you like further clarification or more details?

Here are 5 related questions:

1. How do you convert the vertex form of a quadratic to standard form?
2. Can you always determine the equation of a parabola with just the vertex and one point?
3. What is the significance of the value of $a$ in a quadratic equation?
4. How do you find the axis of symmetry from a quadratic equation?
5. How would the graph change if $a$ were negative?

Tip: The sign of $a$ in the quadratic equation determines whether the parabola opens upwards ($a > 0$) or downwards ($a < 0$).