# What is the right choice for question 20? http://postimage.org/image/md17spw3p/

Asked on by lkballer24

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

The question 20 requests to write the equation of the parabola whose vertex is `(0,-5)`  and it passes through the point `(-4,-13), ` hence, you need to use the vertex form such that:

`f(x) = a(x-h)^2 + k `

h and k are the coordinates of vertex of parabola

Since the problem provides the coordinates of the vertex, you may substitute 0 for h and -5 for k such that:

`f(x) = a(x-0)^2 + (-5)`

`f(x) = ax^2- 5`

Notice that you need to evaluate a, hence, you should use the next information provided by the problem such that:

`f(-4) = -13`

Substituting -4 for x and -13 for f(x) in equation above yields:

`-13 = a*(-4)^2 - 5 => -13 = 16a - 5 => 16a = -13+5`

`16a = -8 => a = -8/16 => a = -1/2`

Hence, evaluating the equation of parabola yields `f(x) = (-1/2)x^2 - 5` , thus, you should select the first answer.

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