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A certain polynomial, P, has a degree of $2$ . Polynomial P has zeros of $2$ and $- 3$ , and $a > 0$ when the function of polynomial P is written in the form of $y = a x^{2} + bx + c$ . Given this information, which of the following could be the graph of polynomial $P ?$

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answer is B.

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Detailed Solution

Given that the quadratic polynomial has zeros as

2

- 3

the form of quadratic polynomial is

a x^{2} + bx + c

function of polynomial,

y = a x^{2} + bx + c

.
This means, at

x = 2

x = - 3,

y

will be zero i.e, the function will take value as zero.
So, according to options given, option (3) and option (4) can be eliminated.
Since, i.e,

a > 0,

the coefficient of

x^{2}

is positive.
At large values of

x

on both sides of

0

(zero), the value of

a x^{2} + bx + c

will be dominated by

a x^{2},

since the term has

x^{2}

in it.
So, for large values of

x

a > 0,

therefore, the parabola must open upwards.
Question Image

Hence, the answer is option 2.

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