Question

find the equation of the parabola with v at the origin,axis x,and passing through(1,-2)

Answer 1

Find the equation of the parabola having vertex $(0,0)$, axis along the $x$-axis and passing through $(2, -1)$.

**Solution:**

The curve must have horizontal orientation, since we know it along the $x$-axis.

So we need to use the general formula

$$y^{2} = 4px$$

We need to find $p$. We know the curve goes through $(2, -1)$, so we substitute:

$$(-1)^{2} = 4(p)(2)$$ $$1 = 8p$$ $$p = \frac{1}{8}$$

So the required equation is

$$y^{2} = \frac{x}{2}$$

**Answer:** $y^{2} = \frac{x}{2}$