SOLUTION: How to solve and graph the quadraic function. Find the vertex, axis and is it wider or narrower than x^2 f(x)= 2x^2+8x+3

Algebra ->  Graphs -> SOLUTION: How to solve and graph the quadraic function. Find the vertex, axis and is it wider or narrower than x^2 f(x)= 2x^2+8x+3      Log On


   

Question 300811: How to solve and graph the quadraic function. Find the vertex, axis and is it wider or narrower than x^2
f(x)= 2x^2+8x+3
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
How to solve and graph the quadraic function. Find the vertex, axis and is it wider or narrower than x^2
%22f%28x%29%22=+2x%5E2%2B8x%2B3


1. Find the x-coordinate of the vertex by evaluating -b%2F%282a%29
2. Find the y-coordinate of the vertex by substituting the value of the 
x-coordinate found in step 1 for x in the equation %22f%28x%29%22=ax%5E2%2Bbx%2Bc
3. The axis of symmetry is the vertical line whose equation is x=-b%2F%282a%29
4. A: If abs%28a%29+%3C+1, the parabola is wider than the graph of the parabola
      whose equation is %22f%28x%29%22+=+x%5E2.  
   B: If abs%28a%29+%3E+1, the parabola is narrower than the graph of the
      parabola whose equation is %22f%28x%29%22+=+x%5E2.

1. -b%2F%282a%29=-%288%29%2F%282%282%29%29=-8%2F4=-2
2. %22f%28-2%29%22=2%28-2%29%5E2%2B8%28-2%29%2B3=2%284%29-16%2B3=8-16%2B3=-5

So the vertex is %22%28-2%2C-5%29%22

3. x=-2
4. abs%282%29%3E1, narrower

The graph of %22f%28x%29%22=2x%5E2%2B8x%2B3 is in red.
The graph of %22f%28x%29%22=x%5E2 is in green. 

graph%28400%2C400%2C-6%2C4%2C-7%2C3%2C2x%5E2%2B8x%2B3%2Cx%5E2%29  

Edwin