Question

plot some quadratic expressions in a graph.
(Any quadratic expressions - your choice)​

Answer 1

Answer:

Step-by-step explanation:

Plot the graph of  

Q

(

x

)

:

2

x

2

+

5

x

+

2

.

Solution:   Step-1:  

a

=

2

>

0

, so the parabola will open upward.

Step-2:  

2

x

2

+

5

x

+

2

=

(

2

x

+

1

)

(

x

+

2

)

, so the zeroes of the expression are  

x

=

−

1

2

,

x

=

−

2

. These are the points where the parabola will cross the horizontal axis.

Step-3: The discriminant is  

D

=

9

(verify). The coordinates of the vertex are  

V

≡

(

−

b

2

a

,

−

D

4

a

)

or  

V

≡

(

−

5

4

,

−

9

8

)

. This will be the lowermost point on the parabola.

Step-4: We calculate  

Q

(

x

)

for some specific values of x. For example,  

Q

(

0

)

=

2

,  

Q

(

−

3

)

=

5

, etc.

Using all this information, the graph can now be plotted easily:

Parabola plotted graph