Question

Let g(x)= -2(3x+4)(x−1)(x−3)^2 be a polynomial function. Name all horizontal and vertical intercepts of the graph. State the end behavior of g.

Answer 1

Answer:

The vertical intercepts is

(4/3,0) (3,0) (1,0)

The horinzontial intercepts is

(0,72)

The end behavior is

as x approaches positive infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches negative infinity.

Step-by-step explanation:

The vertical or y intercepts will be zeroes of the following factors.

$3x + 4 = 0$

$x - 1 = 0$

$(x - 3) {}^{2} = 0$

We solve for x each time.

$x = - \frac{4}{3}$

$x = 1$

$x = 3$

Part B). We need to find the intercepts by setting the equation equal to zero.

The constant expanded will equal 72.

If x=0,

${0}^{y} = 0$

where y is any real number.

So this means all the exponets will equal 0. The constant will just add to the term. so our horinzontal intercept is

$0 + 72 = 72$

Part C) End Behavior

The leading degree is even. Even Degree Polynomials like Quadratics tend to go approach positive infinity vertically as x approaches positive infinity, and as x approaches negative infinity, it approaches positive infinity vertically.

Our leading coefficient is negative so this means our quadratic will get reflected across the x axis.

Now this means, as x approaches positive infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches negative infinity.