Algebra
posted by Cassie .
Without graphing, describe the end behavior of the graph of f(x) = 5X^2  3X + 1
Please explain

it's a parabola opening down.
End behavior should be clear. 
The graph of any function in the form
y = a x ^ 2 + b x + c is a parabola.
A quadratic equationhas two solutions.
In this case :
x 1 = [  3 s qrt ( 29 ) ] / 10
and
x 2 = [  3 + sqrt ( 29 ) ] / 10
If coefficient a is positive then the graph of parabola is concave up.
If coefficient a is negative then the graph of parabola is concave down.
In this case a =  5
That mean parabola is concave down.
Parabolas have a highest or a lowest point (depending on whether they open up or down), called the vertex.
Each parabola has a vertical line of symmetry that passes through its vertex.
The formula for the x  coordinata of a vertex :
h =  b / 2 a
In this case :
h =  (  3 ) / 2 * (  5 )
h = 3 /  10 =  3 / 10
For x =  3 / 10
y =  5 x ^ 2  3 x + 1
y =  5 * ( 3 / 10 ) ^ 2  3 * (  3 / 10 ) + 1
y =  5 * 9 / 100 + 9 / 10 + 1
y =  45 / 100 + 9 / 10 + 1
y =  45 / 100 + 90 / 100 + 100 / 100
y = 145 / 100
y = 5 * 29/ ( 5 * 20 )
y = 29 / 20
Coordinate of vertex (  3 / 10 , 29 / 20 )
P.S.
If you don't know how to solve quadratic equation in google type:
quadratic equation online
When you see list of results click on:
Free Online Quadratic Equation Solver:Solve by Quadratic Formula
When page be open in rectangle type:
5 x ^ 2  3 x + 1 = 0
and click option: solve it
You will see solution stepby step
If you want to see graph of your function in google type:
function graphs online
When you see list of results click on:
rechneronline.de/functiongraphs
When page be open in blue rectacangle type:
 5 x ^ 2  3 x + 1
Then click option : Draw
You will see graph of your function