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Rainbow [258]
3 years ago
9

Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 2, negative 1, and 2

Mathematics
2 answers:
xz_007 [3.2K]3 years ago
6 0
Hello,

A cubic polynomial with -2,1,2 as roots is
f(x)=k*(x+2)(x+1)*(x-2)=k(x²-4)(x+1)=k(x^3+x²-4x-4)

Looking the answers ==>k=1


==>Answer A
vitfil [10]3 years ago
3 0

Answer:

f(x)=x^3+x^2-4x-4

Step-by-step explanation:

Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 2, negative 1, and 2

x intercepts are -2, -1, 2

We write the x intercepts in factor form

f(x)= (x-p)(x-q)(x-r)

where p, q and r  are the x intercepts

f(x)= (x-(-2))(x-(-1))(x-2)

f(x)= (x+2)(x+1)(x-2)

now we multiply the parenthesis using FOIL method

(x+2)(x+1)= x^2 +2x+x+2= x^2+3x+2

f(x)= (x^2+3x+2)(x-2)

now we multiply with (x-2)

x^3-2x^2 +3x^2-6x+2x-4

combine like terms

f(x)=x^3+x^2-4x-4

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2 years ago
Write the equation in slope-intercept form of the line that passes through
mixer [17]

Answer:

We conclude that the equation in slope-intercept form of the line that passes through  (12,9) and is perpendicular to the graph of y = -3/4x + 1 will be:

  • y=\frac{4}{3}x-7

Step-by-step explanation:

We know the slope-intercept form of the line equation

y = mx+b

where

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Given the line

y = -3/4x + 1

comparing with the slope-intercept form of the line equation

The slope = m = -3/4

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:  

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Thus, the slope of the new perpendicular line = – 1/(-3/4) = 4/3

Using the point-slope form

y-y_1=m\left(x-x_1\right)

where m is the slope of the line and (x₁, y₁) is the point

substituting the values of the slope = 4/3 and the point (12, 9)

y-y_1=m\left(x-x_1\right)

y-9=\frac{4}{3}\left(x-12\right)

Add 9 to both sides

y-9+9=\frac{4}{3}\left(x-12\right)+9

y=\frac{4}{3}x-16+9

y=\frac{4}{3}x-7

Therefore, we conclude that the equation in slope-intercept form of the line that passes through  (12,9) and is perpendicular to the graph of y = -3/4x + 1 will be:

  • y=\frac{4}{3}x-7
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