The correct equation for the parabolic curve that passes through the points (-8,0), (0,10), and (8,0) is Equation 3: y = - 5/32 x^2 + 10, as it is the only one that meets all the criteria of the vertex and intersecting points.
The student is asking to determine the equation that correctly represents a parabolic curve passing through the points (-8,0), (0,10), and (8,0).
To find the correct equation, let's analyze each option in relation to the given points:
Equation 1 y = 5/32 x^2 + 10 cannot be right since it does not go through the point (8,0); when x=8, y would be greater than 0.
Equation 2 y = - 5/8 x^2 does pass through (-8,0) and (8,0), but the vertex of this parabola would be at (0,0) and not (0,10).
Equation 3 y = - 5/32 x^2 + 10 does pass through (0,10), and since the coefficient of x^2 is negative, the parabola opens downwards which is consistent with the given points.
When x = 8 or x = -8, y = 0, which fits the description.
Equation 4 y = 5/8 x^2 opens upward and does not correspond to the given points.
Therefore, the equation that matches the curve is Equation 3: y = - 5/32 x^2 + 10
The probable question may be:
The curve start from (-8,0) to (0,10) to (8,0).
Which equation corresponds to the given graph?
1. y= 5/32 x^2+10
2. y= - 5/8 x^2
3. y= - 5/32 x^2+10
4. y= 5/8 x^2