Without the actual image to analyze the specific parabolas, I can provide a general approach on how to determine the number of real solutions for a system of equations consisting of two parabolas.
To find the number of real solutions (i.e., points of intersection) between the two parabolas:
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Identify the Equations: Determine the equations for the solid line parabola and the dotted line parabola. They might be of the form \(y = ax^2 + bx + c\).
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Set the Equations Equal: If you have the equations \(y = f(x)\) and \(y = g(x)\), set them equal to each other to find the points of intersection: \[ ax^2 + bx + c = dx^2 + ex + f \]
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Combine Like Terms: Rearrange the equation to set it to zero: \[ (a-d)x^2 + (b-e)x + (c-f) = 0 \] This is a quadratic equation in the standard form \(Ax^2 + Bx + C = 0\).
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Use the Discriminant: Calculate the discriminant \(D = B^2 - 4AC\):
- If \(D > 0\), there are two distinct real solutions (two points of intersection).
- If \(D = 0\), there is one real solution (the two curves touch at one point).
- If \(D < 0\), there are no real solutions (the curves do not intersect).
By following these steps, you can determine the number of real solutions for the system of equations based on the characteristics of the parabolas. However, without the specific image, I can't give you the exact number. Please check these steps with the specific equations or the visual representation to get the answer.