Question

Without graphing, describe the end behavior of the graph of f(x) = -5X^2 - 3X + 1

Please explain

Answer 1

it's a parabola opening down.
End behavior should be clear.

Answer 2

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 step-by 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/function-graphs

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