SOLUTION: Write the equation of the parabola in both vertex and standard form whose vertex is (-1,-4) and passes through (0,-5). My work was: {{{ y=a(x-h)^2+k }}} Vertex Form {{{ y

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Write the equation of the parabola in both vertex and standard form whose vertex is (-1,-4) and passes through (0,-5). My work was: {{{ y=a(x-h)^2+k }}} Vertex Form {{{ y      Log On


   

Question 1098342: Write the equation of the parabola in both vertex and standard form whose vertex is (-1,-4) and passes through (0,-5).

My work was:

+y=a%28x-h%29%5E2%2Bk+ Vertex Form
+y=a%28x-%28-1%29%29%5E2%2B%28-4%29+ Substituted (-1,-4) into (h,k) values
+-5=a%280%2B1%29%5E2-4+ Substituted (0,-5) into (x,y) values
+-5=a%281%29-4+ Solve for a
+a=-1+
Giving a vertex form of = +y=-%28x%2B1%29%5E2-4+
Finding standard form using +y=-%28x%2B1%29%5E2-4+
+y=-%28x%5E2%2B2x%2B1%29-4+ wasn't sure if I was supposed to distribute the negative here, I didn't
+y=-x%5E2%2B2x%2B1-4+
and I got standard form of = +y=-x%5E2%2B2x-3+
I'm unsure about the procedure, especially with the negative for standard form, but I might be overthinking it, any advice would be appreciated!

Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52900) About Me  (Show Source):
You can put this solution on YOUR website!
.
Write the equation of the parabola in both vertex and standard form whose vertex is (-1,-4) and passes through (0,-5).

My work was: 

 
+y=a%28x-h%29%5E2%2Bk+ Vertex Form

+y=a%28x-%28-1%29%29%5E2%2B%28-4%29+ Substituted (-1,-4) into (h,k) values

+-5=a%280%2B1%29%5E2-4+ Substituted (0,-5) into (x,y) values

+-5=a%281%29-4+ Solve for a 

+a=-1+


Giving a vertex form of = +y=-%28x%2B1%29%5E2-4+


Finding standard form using +y=-%28x%2B1%29%5E2-4+   

+y=-%28x%5E2%2B2x%2B1%29-4+ wasn't sure if I was supposed to distribute the negative here, I didn't     
                              <<<---=== until this line and including this line everything is correct.      


+y=-x%5E2%2B2x%2B1-4+                 <<<---===  This line is WRONG.  It should be  y = -x^2 -2x - 1 - 4 = -x^2 - 2x - 5.

and I got standard form of = +y=-x%5E2%2B2x-3+

---------------------
Your final expression should be   y = -x^2 - 2x - 5.



Answer by josgarithmetic(39630) About Me  (Show Source):