SOLUTION: Find the vertex, axis, and the x & y intercepts of y= (2x-7) (2x-1) please explain step by step I would really appreciate any help!

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the vertex, axis, and the x & y intercepts of y= (2x-7) (2x-1) please explain step by step I would really appreciate any help!      Log On


   

Question 172897: Find the vertex, axis, and the x & y intercepts of
y= (2x-7) (2x-1)
please explain step by step
I would really appreciate any help!
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
y=+%282x-7%29+%282x-1%29+
Expand:
y=4x%5E2-14x-2x%2B7
y=4x%5E2-16x%2B7
Transpose constant to the left, likewise "copy" the "a" constant of a quadratic eqn --->highlight%28a%29x%5E2%2Bbx%2Bcto the left. factor out the right term:
y-7%2B4%2Ahighlight%284%29=4%28x%5E2-4x%29
Complete the square by taking "half" of '4' on the right term,in this ---> 4%2F2=2, then squared it---->2%5E2=4.
y-7%2B16=4%28x%5E2-4x%2Bhighlight%284%29%29
y%2B9=4%28x-2%29%5E2
y=4%28x-2%29%5E2-9 --> it follows vertex form, a%28x-h%29%5E2%2Bk
where--->system%28h=x%2Ck=y%29
So, therefore, the vertex is at (2,-9).
Axis of symmetry is the x-intercept of the vertex: --->highlight%28x=2%29
For Y-Intercept:
F%28x%29=0
y=4%280%29%5E2-14%280%29%2B7
highlight%28y=7%29
For the X-Intercepts: We solve the eqn:
0=4%28x-2%29%5E2-9
9=4%28x-2%29%5E2------>9%2F4=cross%284%29%28x-2%29%5E2%2Fcross%284%29
%2B-sqrt%289%2F4%29=x-2
x=2%2B-1.5 ---->system%28x=2%2B1.5=highlight%283.5%29%2Cx=2-1.5=highlight%280.50%29%29
As you see in the graph:
---->Vertex (2,-9)
Thank you,
Jojo