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Question

Find the nature of the graph of the following quadratic equation in terms of which side it will open.

I. y = x2 8x a. open upward
II. y = 2x2 + 3 b. open downward
III. y = x2 6x + 4 c. open right
d. open left

A
Ia, IIb, IIIa
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B
Ia, IIc, IIId
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C
Ia, IIa, IIIa
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D
Ia, IIb, IIIb
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Solution

The correct option is A Ia, IIb, IIIa
Comparing with standard quadratic equation y = ax2 + bx + c, we get a=1, b=8, c =0.
Since the leading coefficient a =1 > 0, hence the graph will open upwards.

Comparing with standard quadratic equation y = ax2 + bx + c, we get a=2, b=0, c =3.
Since the leading coefficient a = 2 < 0, hence the graph will open downwards.

Comparing with standard quadratic equation y = ax2 + bx + c, we get a=1, b=6, c = 4
Since the leading coefficient a =1 > 0, hence the graph will open upward.

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