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From the graph of a quadratic polynomial...

From the graph of a quadratic polynomial `y=ax^(2)+bx+c, a,b, epsilonR` , Find its vertex, roots and D.

A

`b^(2)-4aclt0`

B

`c/alt0`

C

`c` is negative

D

Abscissa corresponding to the vertex is `(-b/(2a))`

Text Solution

Verified by Experts

The correct Answer is:
B
Here `a lt 0`
Cut off Y-axis `x=0`
`impliesy=clt0` [from graph]
`:.clt0`
x -coordinate of vertex `gt0`
`implies-b/(2a)gt0`
`impliesb/alt0`
But `alt0`
`:.bgt0`
any y-coordinate of vertex `lt0`
`implies-D/(4a)lt0impliesD/(4a)gt0`
`impliesDlt0 [ :' alt0]`
i.e. `b^(2)-4aclt0`
`:.c/agt0 [:'clt0, alt0]`
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