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# Line L, given by the graph of y=5x+6, intersects the graph of y=x^2 at two points P=(a,b) and Q=(c,d), such that a

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Line L, given by the graph of y=5x+6, intersects the graph of y=x^2 at two points P=(a,b) and Q=(c,d), such that a

Aug 8, 2023

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I think that you left something out....   Aug 8, 2023
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Hello,

The line L, represented by the equation y = 5x + 6, intersects the graph of y = x^2 at two distinct points P and Q. Analyzing the equations, we can find the intersection points by equating the expressions for y:

Substituting y from the equation of line L into the equation of the parabola, we get: 5x + 6 = x^2.

Rearranging the equation gives the quadratic equation: x^2 - 5x - 6 = 0.

Solving the quadratic equation yields two values for x: a and c.  TKMaxxCare

Substituting these x-values back into the equation of line L, we find the corresponding y-values: b and d.

The resulting points P(a, b) and Q(c, d) are the intersection points of the line and the parabola. The line intersects the parabola at these points due to their shared coordinates (x, y). The solution ensures that a < c, as the line starts below the parabola and then crosses it. Thus, the line L intersects the graph of y = x^2 at the distinct points P and Q, satisfying the given conditions.

I hope the information may helps you.

Aug 10, 2023