To write the equation of the quadratic function in standard form, we need to identify the key components from the graph you described, such as the vertex of the parabola and its direction (opening upwards or downwards), as well as any specific points on the parabola. However, since I cannot see the image you referred to, I will guide you on how to find the equation based on the information you should observe from the graph.
The standard form of the quadratic function is given by:
\[ y = ax^2 + bx + c \]
Here’s how to determine the coefficients \(a\), \(b\), and \(c\):
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Identify the Vertex: Look at the graph to find the vertex of the parabola. The x-coordinate of the vertex can be used in the equation.
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Determine the Direction: If the parabola opens upwards, \(a\) will be positive; if it opens downwards, \(a\) will be negative.
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Select Another Point: Find at least one additional point on the parabola (let's call it \((x_1, y_1)\)) that you can use to substitute into the equation to help find the coefficients.
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Substitute Vertex in Vertex Form: The vertex form of a quadratic equation is: \[ y = a(x - h)^2 + k \] where \((h, k)\) is the vertex.
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Convert to Standard Form: If you use the vertex form, expand and rearrange the equation to get it into standard form.
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Find \(b\) and \(c\): Using another point on the parabola, substitute the coordinates into the equation to form a system of equations. You can then solve for \(a\), \(b\), and \(c\).
If you can provide specific coordinates from the graph (like the vertex and another point), I could help you determine the exact equation!