To write the standard form of the quadratic function $y = ax^2 + bx + c$ for the graph shown, let's analyze the given points.

The parabola has:

• A vertex at $(0, -4)$, indicating that this is the minimum point.
• Another point at $(-1, -5)$, which we can use to determine the coefficient $a$.

Since the vertex is at $(0, -4)$, the equation can start as: $y = ax^2 - 4$ Now, using the point $(-1, -5)$, substitute $x = -1$ and $y = -5$ to solve for $a$: $-5 = a(-1)^2 - 4$ $-5 = a - 4$ $a = -1$

Thus, the equation of the quadratic function is: $y = -x^2 - 4$

Would you like further details or have any questions?

Related Questions

1. How do you determine the direction of a parabola based on its equation?
2. What is the role of the vertex in the standard form of a quadratic equation?
3. How can you rewrite this equation in vertex form?
4. How does the value of $a$ affect the width of the parabola?
5. What are the steps to convert a quadratic equation from standard to vertex form?

Tip:

Remember, the sign of $a$ determines whether the parabola opens up or down!