<PRE><B>Question 1146110</B>
&lt;br&gt;
As in the response from the other tutor, a vertex at (-3,-2) means the equation is of the form&lt;br&gt;
{{{y-(-2) = a(x-(-3))^2}}}&lt;br&gt;
or&lt;br&gt;
{{{y+2 = a(x+3)^2}}}&lt;br&gt;
or&lt;br&gt;
{{{y = a(x+3)^2-2}}}&lt;br&gt;
Then here is a different way to determine the value of the constant a to complete the equation.&lt;br&gt;
Note that the constant a determines how steep the parabola is.&lt;br&gt;
Then note that the given point on the parabola is 3 units to the right of the vertex and 9 units up from the vertex.&lt;br&gt;
Then, since 9 is 3^2, you know the constant a is 1, so the equation is&lt;br&gt;
{{{y = (x+3)^2-2}}}
{{{y = (x^2+6x+9)-2}}}
{{{y = x^2+6x+7}}}&lt;br&gt;
Let&#39;s look again at this method for determining the value of the constant a in the equation.&lt;br&gt;
Suppose the given point were (1,6).&lt;br&gt;
That point is 4 to the right of the vertex and 8 units up from the vertex.&lt;br&gt;
Since 4^2 is 16 and the point is only 8 units up from the vertex, the value of the constant a is 8/16 = 1/2.&lt;br&gt;
And one more example, to help you try to see how this method works.&lt;br&gt;
This time the given point is (-1,10).  That point is 2 to the right and 12 up from the vertex.  Since 2^2 is 4, the value of the constant a is 12/4 = 3.</PRE>