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Which is an equation for the parabola that has vertex (-3, 1) and passes through the point (-2, 4)?

 Apr 7, 2020
 #1
avatar+111329 
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The  vertex form is

 

y  = a(x - h) ^2  +  k           where (h, k)  is  the  vertex  and (x,y) is a point on the graph

 

So

 

4 = a ( -2-  -3)^2 + 1              subtract 1 from both sides

 

3 = a ( 1)^2

 

3  = a (1)

 

a  = 3

 

So...the equation is

 

y = 3 ( x + 3)^2  + 1

 

 

cool cool cool

 Apr 7, 2020
 #2
avatar+932 
+1

The equation of the parabola with vertex (h,k)(h,k) is y=a(−h+x)^2+ky=a(−h+x)^2+k.

Thus, the equation of the parabola is y=a(x+3)^2+1y=a(x+3)^2+1.

To find a, use the fact that the parabola passes through the point (−2,4)(−2,4): 4=a+14=a+1.

Solving this equation, we get that a=3a=3.

Thus, the equation of the parabola is y=3(x+3)2+1y=3(x+3)^2+1.

 

I used parabola calculator.

 

Hope it helps!

 Apr 7, 2020
edited by HELPMEEEEEEEEEEEEE  Apr 7, 2020

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