Equation of parabola from graph
Transformed equation of parabola is:
\(y=af(x-h)^2+k\) \(……(1)\)
Where \(a=\)Vertical stretch or compression,
\(h=\)horizontal shift (left or right)
\(k=\)Vertical shift (up or down)
From graph, \(h=3\) and \(k=-2\);
plug \(h\) and \(k\) values in eqn \((1)\)
\(y=a(x-3)^2-2\) /(……(2)\)
To find \(‘a’\), use the given point \((1,0)\) as:
\(0=a(5-3)^2-2\)
\(0=4a-2\)
\(a=1/2\);plug in eqn.(2)
\(y=1/2 (x-3)^2-2\);which is the reqd.eqn.