To determine the equation of the concave up parabola passing through the 1st and 4th quadrants on the given coordinate plane, we can analyze the options provided.
A concave up parabola typically has a form like \(y = a(x - h)^2 + k\), where:
- \(a > 0\) indicates the parabola opens upwards,
- \((h, k)\) is the vertex of the parabola.
Let's break down the options:
- \(y = 2(x−5)^2−3\): This is a concave up parabola with vertex at (5, -3).
- \(y = 3(x−5)^2−3\): This is also a concave up parabola with vertex at (5, -3).
- \(y = (x−5)^2−3\): This is again a concave up parabola with the same vertex at (5, -3).
- \(y = −(x−3)^2−5\): This is a concave down parabola, so this option does not match.
Since the parabola is stated to be concave up, the first three options are potential candidates.
To find which one fits, we must check for other characteristics such as the vertex and any points it may pass through, but this is not given in the question. Assuming the parabola is centered at \((5, -3)\) based on the vertex format and shape, all three concave up options would work.
Without unique points identified from the graph, determining which equation is most accurate would require more context. As such, we can confirm only that the equations from choices 1, 2, and 3 are correct formats for a concave up parabola.
If you need to select one equation based on the function shapes provided, I would suggest going with the simplest form which may describe the graph, which is:
\(y = (x−5)^2−3\).
This version has smaller coefficients and highlights the vertex structure without complicating its scaling factor, making it a likely candidate for a standard equation of the given graph.