To write the equation of a quadratic function in standard form (y = ax² + bx + c), we need more information than just a single point. A quadratic function typically requires at least one more piece of data, whether it be another point on the graph or information about the vertex or the direction of the parabola (i.e., whether it opens upwards or downwards).
However, if you meant that the vertex of the quadratic is at the point (-2, 5), we can use the vertex form of a quadratic function, which is:
\[ y = a(x - h)^2 + k \]
where (h, k) is the vertex of the parabola. Here, the vertex is (-2, 5), so h = -2 and k = 5. The equation will be:
\[ y = a(x + 2)^2 + 5 \]
To convert this to standard form, we need the value of "a." Without that information, we can't find a unique quadratic equation. However, if we let’s assume a = 1 for simplicity, then:
\[ y = (x + 2)^2 + 5 \]
Expanding this:
\[ y = (x^2 + 4x + 4) + 5 \] \[ y = x^2 + 4x + 9 \]
So, if \( a = 1 \), the standard form of the quadratic function would be:
\[ y = 1x^2 + 4x + 9 \]
This gives us:
- \( _ = 1 \)
- \( _ = 4 \)
- \( _ = 9 \)
To summarize, if the vertex is (-2, 5) and assuming \( a = 1 \), the equation in standard form would be:
\[ y = 1x^2 + 4x + 9 \]
If you have a specific value for "a" (the coefficient), please provide it for a more accurate equation!
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