SOLUTION: Write an equation for the parabola in standard form. Use a graphing utility to graph the equation and verify your result. f(x) = Point: (0,7) Vertex:(-3,-2)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Write an equation for the parabola in standard form. Use a graphing utility to graph the equation and verify your result. f(x) = Point: (0,7) Vertex:(-3,-2)      Log On


   

Question 1146110: Write an equation for the parabola in standard form. Use a graphing utility to graph the equation and verify your result.
f(x) =
Point: (0,7)
Vertex:(-3,-2)
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


As in the response from the other tutor, a vertex at (-3,-2) means the equation is of the form

y-%28-2%29+=+a%28x-%28-3%29%29%5E2

or

y%2B2+=+a%28x%2B3%29%5E2

or

y+=+a%28x%2B3%29%5E2-2

Then here is a different way to determine the value of the constant a to complete the equation.

Note that the constant a determines how steep the parabola is.

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.

Then, since 9 is 3^2, you know the constant a is 1, so the equation is

y+=+%28x%2B3%29%5E2-2
y+=+%28x%5E2%2B6x%2B9%29-2
y+=+x%5E2%2B6x%2B7

Let's look again at this method for determining the value of the constant a in the equation.

Suppose the given point were (1,6).

That point is 4 to the right of the vertex and 8 units up from the vertex.

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.

And one more example, to help you try to see how this method works.

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.