Question

draw the graph of (2x-1)sqr=8y-3

Answer 1

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Answer 2

Solution-

Given equation,

$\Rightarrow (2x-1)^2=8y-3$

$\Rightarrow (2(x-\frac{1}{2}))^2=8y-3$

$\Rightarrow 4(x-\frac{1}{2})^2=8y-3$

$\Rightarrow (x-\frac{1}{2})^2=\frac{8y-3}{4}$

$\Rightarrow (x-\frac{1}{2})^2=\frac{8y}{4}-\frac{3}{4}$

$\Rightarrow (x-\frac{1}{2})^2=2y-\frac{3}{4}$

$\Rightarrow (x-\frac{1}{2})^2=2(y-\frac{3}{8})$

Comparing this to the general parabola equation with vertex at (h, k) and focus p,

$(x-h)^2=4.p.(y-k)$

So,

$h=\frac{1}{2}=0.5,\ k=\frac{3}{8}=0.375,\ p=\frac{1}{2}=0.5$

Therefore, its vertex (h, k) will be at (0.5, 0.375) and focus (h, k+p) will be at (0.5, 0.875). Here the axis of symmetry is x=0.5