SOLUTION: Graph each quadratic function Where is the line of symmetry for any function of the form f(x) = ax^2 + c? What is the equation for this line?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Graph each quadratic function Where is the line of symmetry for any function of the form f(x) = ax^2 + c? What is the equation for this line?      Log On


   

Question 1030247: Graph each quadratic function
Where is the line of symmetry for any function of the form f(x) = ax^2 + c? What is the equation for this line?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The x-value of the line of symmetry is:
+x%5Bs%5D+=+-b%2F%282a%29+
If the equation is:
+f%28x%29+=+a%2Ax%5E2+%2B+c+
instead of
+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
then:
+b+=+0+ and
+x%5Bs%5D+=+-0%2F%282a%29+
+x%5Bs%5D+=+0+
----------------
The axis of symmetry is a vertical line
+x+=+0+
----------------
Check:
suppose
+a+=+5+
+c+=+2+
Here's the plot:
+graph%28+400%2C+400%2C+-4%2C+4%2C+-4%2C+10%2C+5x%5E2+%2B+2+%29+
Neither +a+ nor +c+
had any effect on the axis of symmetry
in this case, which is +x+=+0+