((Look at the image))

  a)  y = 2x⁴ -18x² +8x +24

  b)  4th degree; tends toward +∞ when |x| gets large

Step-by-step explanation:

a) When r is a root of the polynomial, (x -r) is a factor. The given roots mean the factors are ...

  y = a(x -(-1))(x -(-3))(x -2)(x -2) = a(x+1)(x+3)(x-2)²

The product of the constant terms is a(1)(3)(2²) = 12a. This is the y-intercept, which is said to be 24. So ...

  12a = 24   ⇒   a = 2

The polynomial function is then ...

  y = 2(x +1)(x +3)(x -2)²

  y = 2x⁴ -18x² +8x +24

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b) The leading coefficient of this 4th-degree polynomial is positive, so when x has large positive or negative values, the function value will tend toward positive infinity.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.