Question

The above quadratic function can model the natural shape of a banana. Now we

know that a parabolic shape must have a quadratic function, therefore an equation

in standard form of f(x) = ax2 +bx +c. To find an equation for the parabolic

shape of the banana we need to find the values of a, b and c. From the banana

picture above, we can see that a quadratic function is able to model the banana

quite accurately, with a = 0.1, b = 0 and c = 0. Therefore, the equation is f(x) =

0.1 x2



Now answer the following questions:-

(i)Name the shape of the banana curve from the figure.

(ii)Find the number of zeros of the polynomial for the shape of the banana.

(iii) If the curve of the banana is represented by f(x)= x2

-x-12, find its zeroes.

(iv)If the representation of banana curves whose one zero is four and sum of

zeroes is zero then find the quadratic polynomial.

(v)What will be the shape of the banana curve if a is negative​

Answer 1

Answer:

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Answer 2

Answer:

i) A parabola is formed with the curve of banana

ii) Since the line intersects on the x-axis. Therefore number of zeroes is 1

iii) sum of Zeroes= 0therefore, alpha + beta = 0 

Step-by-step explanation:

For the Third part:-f(x) = x²-x-12

= x²+3x-4x-12

=x(x+3)-4(x+3)

=(x-4)(x+3)

∴ x-4=0  or  x+3=0

∴ x=4 or x=-3

∴ α=4 and β= -3

therefore the other zero is -3

And both the zeroes are 4 and -3.