# How do you write the vertex form of the equation of the parabola which has a vertex of (0,0) and contains the point (2,-2)?

Jul 4, 2016

The equation of parabola is $y = - \frac{1}{2} \cdot {x}^{2}$

#### Explanation:

The equation of parabola having vertex at $0 , 0$ is $y = a {\left(x - 0\right)}^{2} + 0 \mathmr{and} y = a \cdot {x}^{2}$. The parabola contains the point$\left(2 , - 2\right) \therefore - 2 = a \cdot {2}^{2} \mathmr{and} a = - \frac{1}{2}$. Putting the value of "a" in the equation of parabola we get $y = - \frac{1}{2} \cdot {x}^{2}$ graph{(-1/2)*x^2 [-10, 10, -5, 5]}[Ans]