Factor completely please
2 answers:
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Answer:
vertex = (- 1, - 4.5 )
Step-by-step explanation:
Given
f(x) = (x - 2)(x + 4)
The vertex lies on the axis of symmetry which is positioned at the midpoint of the zeros.
To find the zeros let f(x) = 0, that is
(x - 2)(x + 4) = 0
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x + 4 = 0 ⇒ x = - 4
The x- coordinate of the vertex is therefore
x = =
= - 1
Substitute x = - 1 into f(x) for corresponding y- coordinate
f(- 1) = (- 1 - 2)(- 1 + 4) =
× - 3 × 3 = 0.5 × - 9 = - 4.5
Coordinates of vertex = (- 1, - 4.5 )
Since the two fractions have a common denominator already, we can just subtract the numerators.
b-3b=-2b or -3b+b=-2b
Either way you get the same answer :)
Our new fraction is
Now we know that this must be equal to
Again, since the denominators are already the same of course they are equal. 13=13
Now we have to set the numerators equal
-2b=8
Use inverse operations to get b alone
-2b=8
÷-2 ÷-2
b=-4
If you have any questions, feel free to ask. Hope this helped! :)
Answer: see image
<u>Step-by-step explanation:</u>
Count how many spaces the vertex is away from the line x = -1. Then place that vertex the same distance on the other side of the line x = -1.
