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}}}
<pre><font size = 4 color = "indigo"><b>

1. Find the x-coordinate of the vertex by evaluating {{{-b/(2a)}}}
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 {{{"f(x)"=ax^2+bx+c}}}
3. The axis of symmetry is the vertical line whose equation is {{{x=-b/(2a)}}}
4. A: If {{{abs(a) < 1}}}, the parabola is wider than the graph of the parabola
      whose equation is {{{"f(x)" = x^2}}}.  
   B: If {{{abs(a) > 1}}}, the parabola is narrower than the graph of the
      parabola whose equation is {{{"f(x)" = x^2}}}.

1. {{{-b/(2a)=-(8)/(2(2))=-8/4=-2}}}
2. {{{"f(-2)"=2(-2)^2+8(-2)+3=2(4)-16+3=8-16+3=-5}}}

So the vertex is {{{"(-2,-5)"}}}

3. {{{x=-2}}}
4. {{{abs(2)>1}}}, narrower

The graph of {{{"f(x)"=2x^2+8x+3}}} is in red.
The graph of {{{"f(x)"=x^2}}} is in green. 

{{{graph(400,400,-6,4,-7,3,2x^2+8x+3,x^2)}}}  

Edwin</pre>