SOLUTION: y=x^2+6x+3 What is the axis of symmetry? x=x= Compute the coordinates of the vertex: (( , )) compute the yy-intercept as a point: (( , )) find the point symmetric to the yy-interce

Algebra ->  Test -> SOLUTION: y=x^2+6x+3 What is the axis of symmetry? x=x= Compute the coordinates of the vertex: (( , )) compute the yy-intercept as a point: (( , )) find the point symmetric to the yy-interce      Log On


   

Question 1159758: y=x^2+6x+3 What is the axis of symmetry? x=x= Compute the coordinates of the vertex: (( , )) compute the yy-intercept as a point: (( , )) find the point symmetric to the yy-intercept
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Put the equation in vertex form: y+=+a%28x-h%29%5E2%2Bk

In that form, the vertex is at (h,k), and the axis of symmetry is x=h.

Complete the square....

x%5E2%2B6x%2B3+=+%28x%5E2%2B6x%2B9%29%2B3-9+=+%28x%2B3%29%5E2-6

This form of the equation tells us that the vertex is at (-3,-6) and the axis of symmetry is x=-3. That can be seen in the graph:

graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2%2B6x%2B3%29

For the y-intercept, set x=0 and evaluate. Using the given form of the equation, it is easy to see that the y-intercept is (0,3).

The y-intercept is 3 units to the right of the axis of symmetry; the point symmetric with the y-intercept will be 3 units to the left of the axis of symmetry, and it will have the same y value as the y-intercept: (-6,3). That is also easily seen in the graph.