SOLUTION: Write the standard form of the equation of the parabola that has the indicated vertex and passes through the given point. (Let x be the independent variable and y be the dependent

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Write the standard form of the equation of the parabola that has the indicated vertex and passes through the given point. (Let x be the independent variable and y be the dependent       Log On


   

Question 1117778: Write the standard form of the equation of the parabola that has the indicated vertex and passes through the given point. (Let x be the independent variable and y be the dependent variable.)
a. Vertex (-4,9); Point (0,25)
b. Vertex (-2,9); Point (-5,0)
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


a. With vertex (-4,9) and y the dependent variable, the equation is

y-9+=+a%28x%2B4%29%5E2

Plug in the x and y values of the given point to determine the value of the constant a.

25-9+=+a%280%2B4%29%5E2
16+=+16a
a+=+1

The equation is

y-9+=+%28x%2B4%29%5E2 or y+=+%28x%2B4%29%5E2%2B9

b. Use the same strategy.

Vertex (-2,9), so the equation is y-9=a%28x%2B2%29%5E2.

Plug in (x,y)=(-5,0) to determine the value of a.

0-9+=+a%28-5%2B2%29%5E2
-9+=+9a
a+=+-1

Equation: y-9+=+-%28x%2B2%29%5E2 or y+=+-%28x%2B2%29%5E2%2B9