Question

The graph of the quadratic polynomial ax2 + bx + c, (e.g. x2 + 5x + 6), a <0, b > 0, c > 0, a, b, c,a,b,c belongs to R​

Answer 1

Answer:

Step-by-step explanation:

ax²+bx+c

If a>0 then the graph open upwards

If a < 0 then the graph open downwards

here a<0 then graph open downwards

Now D = b²-4ac

If D>0 Then the graph cuts x axis in 2 distinct points

If D=0 Then the graph touches the x axis at one point

If D<0 Then the graph does not interact with x axis

Here b² > 0 and a<0 and c> 0 so ac<0 so -4ac>0

Something (b²) positive added to something positive (-4ac) is always positive

So D>0 so graph cuts x axis in two distinct points

Sum of roots = -b/2a is positive and product is negative (c/a)

So the graph cuts x axis in both +ve and -ve x axis and +ve part is greater than negative part.

for x = 0 the graph cuts y axis and f(0) = c and c> 0 so the graph cuts the +ve y axis

Vertex of graph = (-b/2a,-D/4a)

Here -b/2a and -D/4a both are positive so vertex lies in first quadrant

Thus now we know everything about graph.

Might Help, Thanks!

Some examples might help!

Answer 2

what is R ?

Step-by-step explanation:

can u plz explain ??