For the quadratic, y = 3x2 + 4x - 3, the y-intercept is

Step-by-step explanation:

To complete the square of

−

3

x

2

+

4

x

−

3

:

Take out the

−

3

y

=

−

3

(

x

2

−

4

3

x

)

−

3

Within the brackets, divide the second term by 2 and write it like this without getting rid of the second term:

y

=

−

3

(

x

2

−

4

3

x

+

(

2

3

)

2

−

(

2

3

)

2

)

−

3

These terms cancel each other out so adding them to the equation isn't a problem.

Then within the brackets take the first term, the third term, and the sign preceding the second term, and arrange it like this:

y

=

−

3

(

(

x

−

2

3

)

2

−

(

2

3

)

2

)

−

3

Then simplify:

y

=

−

3

(

(

x

−

2

3

)

2

−

4

9

)

−

3

y

=

−

3

(

x

−

2

3

)

2

+

4

3

−

3

y

=

−

3

(

x

−

2

3

)

2

−

5

3

You can conclude from this that the vertex is

(

2

3

,

−

5

3

)

the thermometer is precise but not accurate

step-by-step explanation: