Student estimates, then calculates exactly and symbolically the value of $k$ for a parabola $y = k x^2$ which passes through a given point.
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\nThe equation for a parabola with vertex at the origin is given by the general equation
\n$y=kx^2$.
\nThis equation describes an infinite family of parabolas, each corresponding to a different value of $k$.
\n", "advice": "Substituting in the known coordnates of the point into the equation of the parabola for $k$ gives:
\n$k = \\dfrac{y}{x^2} = \\dfrac{\\var{A[1]}}{\\var{A[0]}^2} = \\var{sigformat(k,3)}$.
\nThe value of $k$ for a parabola passing through the point $(\\var{b}, \\var{h})$ is determined the same way, and the resulting equation for the parabola is
\n$y= \\dfrac{\\var{h}}{\\var{b}^2}\\; x^2$
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\n$k_{est} = $ [[0]]
\nNow substitute the coordinates of the known point into the equation of the parabola and solve for the exact value of $k$ to three significant figures.
\n$k =$ [[1]]
Determine the equation for a parabola with a vertex at the origin, which passes through a known point located at $(\\var{b}, \\var{h})$.
$y =$ [[2]]
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