To determine the equation of the parabola represented in the graph, we need to analyze the given options. Since the parabola is described as being concave up, we will focus on forms of equations that have positive coefficients for the squared term.
The general form of a parabola that opens upwards is:
\[ y = a(x - h)^2 + k \]
where (h, k) is the vertex of the parabola.
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Examine the options:
- Option 1: \( y = - (x - 3)^2 - 5 \) (concave down)
- Option 2: \( y = 3(x - 5)^2 - 3 \) (concave up)
- Option 3: \( y = (x - 5)^2 - 3 \) (concave up)
- Option 4: \( y = 2(x - 5)^2 - 3 \) (concave up)
Since the parabola is concave upwards, we can ignore the first option.
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Determine the vertex: The given options suggest that the vertex might be around \( x = 5 \) and \( y = -3 \), as options 2, 3, and 4 have this form.
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Y-values at specific x-values: You may want to confirm which one of the upward-opening parabolas fits best with the graph. If we cannot see the graph, we can use the vertex from the given options.
Without the graph visible, we generally can conclude that all options from 2 to 4 have reasonable formats for the vertex form of a parabola that opens upward. If you're looking at the height/width characteristics as well, you can choose between these three.
Conclusion: If the parabola passes through the y-axis at -3 (like in options 2, 3, or 4), it could very well be:
- If it’s wider, then use option 3 or 4.
- If it's still reasonably narrow then option 2.
Ultimately, it would depend on the specifics of the graph. However, given typical context and notation, if the point of interest is at:
- \( (5, -3) \), the equation might be \( y = (x - 5)^2 - 3 \).
Thus, if one is limited to confirmative choices and without additional graph details, the best option would be:
\( y = (x - 5)^2 - 3 \) which corresponds to Option 3.