Question

the graph of quadratic polnomial is always a​

Answer 1

Step-by-step explanation:

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The graph of quadratic polynomial is always parabola

The parabola can be of two types

a) upward parabola

a) downward parabola

And there will be there cases in both a) and b)

1) Parabola above/below the x-axis

2) Parabola just touches x-axis

3) Parabola intersecting x-axis

If parabola which is above/below x-axis has imaginary roots

If the parabola which just touches x-axis will have just both roots to be real and equal

If the parabola cuts/intersects x-axis the it has both roots to be real and distinct

Let's evaluate more using General equation

a x²+b x + c = 0

For upward parabola a is +ve

For downward parabola a is -ve

Where c is Y-intecept

For imaginary roots, D < 0

For real and equal roots D = 0

For real and unequal roots D > 0

The uppermost part of downward parabola is given by (-b/2a , -D/4a)

The lower-most part of upward parabola is given by (-b/2a , -D/4a)

Where D = Discriminant