# How do you write standard form of equation of the parabola that vertex is (2,3) and graph passes through the given point (0,2)?

Mar 19, 2018

The equation of parabola is $y = - \frac{1}{4} {\left(x - 2\right)}^{2} + 3$.

#### Explanation:

The vertex form of equation of parabola is

y = a(x-h)^2+k ; (h,k) being vertex , here $h = 2 , k = 3$

So the equation of parabola is y = a(x-2)^2+3 ;. The parabola

passes through point $\left(0 , 2\right) \therefore$ the point will satisfy the equation

of parabola. Putting $x = 0 \mathmr{and} y = 2$ in the equation we get,

$2 = a {\left(0 - 2\right)}^{2} + 3 \mathmr{and} 2 = 4 a + 3 \mathmr{and} 4 a = 2 - 3$or

$4 a = - 1 \mathmr{and} a = - \frac{1}{4}$. Hence ,the equation of parabola is

$y = - \frac{1}{4} {\left(x - 2\right)}^{2} + 3$.

graph{-1/4(x-2)^2+3 [-10, 10, -5, 5]} [Ans]