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

)

add an image !

step-by-step explanation:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.