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

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Answer 1 · 2016-03-02T18:06:17

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

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:

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

Challenge problem:

Find the equation of the quadratic function that passes through #(2, 3), (3, -7) and (-9, 1)#