# How do you write the equation of the parabola in vertex form given vertex (2,-1) and a point (0,3)?

Mar 2, 2016

You must plug these points into their respective parameters in vertex form.

#### Explanation:

Vertex form is of the form $y = a {\left(x - p\right)}^{2} + q$

Your point (0,3) should be plugged into (x, y). Your vertex (2, -1) should be imputed as (p, q). As a result, we are solving for a.

$3 = a \left(0 - 2\right) - 1$

$3 = - 2 a - 1$

$3 + 1 = - 2 a$

$4 = - 2 a$

$- 2 = a$

The equation is $y = - 2 \left(x - 2\right) - 1$

Practice exercises:

1. The following graph shows a quadratic function. Find its equation.

graph{y = 2x^2 + 4x - 6 [-20, 20, -10, 10]}

1. A graph has a vertex at (-2,4) and passes through (-7,-6). Find its equation.

Challenge problem:

Find the equation of the quadratic function that passes through $\left(2 , 3\right) , \left(3 , - 7\right) \mathmr{and} \left(- 9 , 1\right)$