Question

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

Answer 1

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

Explanation:

Vertex form is of the form `y = a(x - p)^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(0 - 2) - 1`

`3 = -2a - 1`

`3 + 1 = -2a`

`4 = -2a`

`-2 = a`

The equation is `y = -2(x - 2) - 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 `(2, 3), (3, -7) and (-9, 1)`