Monday

November 24, 2014

November 24, 2014

Posted by **Misty** on Thursday, September 15, 2011 at 11:39am.

the polynomial function -x^4 - 4x^2. That is -x to the fourth power minus -4x squared. Please Help!!!

- Pre-calculus -
**Anonymous**, Wednesday, September 21, 2011 at 4:52pmMethod 1: use a graphing tool and enter the function.

Method 2: Using several values for x, evaluate the function and plot the points (x,f(x)) to see the shape of the curve.

If you can't evaluate f(x), then you might reconsider taking pre-calculus.

As a starting point, note that f = -x^2(x^2+4), so you know there is a double root at x=0, so the graph is tangent to the x-axis at (0,0). Since it's a quartic, as x gets large, f gets large negative. Since there are no other real roots, the graph may look kind of like a flattened parabola opening downward. That will be the case here if f(x) < 0 for x near 0. Indeed, f(x) < 0 near x=0, so we know the graph is tangent to the x-axis from below.

FYI: Quartics may also look like a rounded W shape, But since the graph opens down, and is tangent below the x-axis, there can't be any bumps nearby, because then the graph would cross the x-axis near x=0. That would mean there are real roots.

**Answer this Question**

**Related Questions**

Algebra 1--Step-by-Step - Can someone show me how to solve these step-by-step? ...

Algebra - x^2+6x-44/x+9 X squared plus six X minus 44 divided by X+9. Having a ...

pre calculus - find the following for the function f(x)=(x+3)^2(x-1)^2 a.) find ...

Calculus - Sketch a graph of a function f(x) that is differentiable and that ...

Calculus - Use the four-step process to find the slope of the tangent line to ...

Algebra 2 - can someone show me how to do it step by step please! Use a graph ...

Physics - Can someone please show me step by step how to normalize e^-5x in the ...

real-life step function - So if I wanted to do a step-function graph for gas ...

math - I dont understand this calculus problem at all. can someone show me step ...

Algebra help+check please? - Graph the function. Compare the graph with the ...