The vertex of this parabola is at (2,-4). When the y-value is -3, the x-value -3. What is the coefficient of the squared term in the parabola's equation?

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Answer 1 · 2018-06-23T18:07:36

There are two parabolas that meet your specifications.

The first parabola is of the form:

$y = a_1(x-2)^2-4$

The second parabola is of the form:

$x = a_2(y- -4)^2+2$

Find the value of $a_1$ by substituting $y(-3) = -3$ :

$-3 = a_1(-3-2)^2-4$

$1 = a_1(-3-2)^2$

$a_1 = 1/25$

Find the value of $a_2$ by substituting $x(-3) = -3$ :

$-3 = a_2(-3- -4)^2+2$

$a_2 = -5$

The two equations that meet your requirements are:

$color(red)(y = 1/25(x-2)^2-4)$ and $color(blue)(x = -5(y- -4)^2+2)$

Please observe that both parabolas have their vertex at $(2,-4)$ and contain the point $(-3,-3)$ :

![www.desmos.com/calculator](useruploads.socratic.org)