SOLUTION: A parabola has an x-intercept at 2, its axis of symmetry is the line x = 4, and the y- coordinate of its vertex is 6. Determine the equation of the parabola. Hint: The equation lo

Question 402781: A parabola has an x-intercept at 2, its axis of symmetry is the line x = 4, and the y- coordinate of its vertex is 6. Determine the equation of the parabola. Hint: The equation looks like y = ax^2+bx+c. Use the given information to figure out what a, b, c must be. For example, when x = 2, the y value must be 0 since 2 is an x-intercept. That means 0 = 4a + 2b + c. The other two given facts provide similar information about a, b, c.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A parabola has an x-intercept at 2, its axis of symmetry is the line x = 4, and the y- coordinate of its vertex is 6.
-------------------
Determine the equation of the parabola. Hint: The equation looks like y = ax^2+bx+c.
-------------------
Use the given information to figure out what a, b, c must be. For example, when x = 2, the y value must be 0 since 2 is an x-intercept. That means 0 = 4a + 2b + c. The other two given facts provide similar information about a, b, c.
-----
x-int: (6,0)
axis of symmetry: -b/2a = 4
Vertex: (0,6)
------
Form: y = ax^2+bx+c
---
(6,0) implies 36a+6b+c = 0
---
axis implies 8a + b + 0 = 0
----
vertex implies 0 + 0 + c = 6
-------------------------------
Since c = 6 you get:
36a+6b = -6
8a + b = 0
------
Modify:
6a+b = -1
8a+b = 0
------------
Subtract to solve for "a":
2a = 1
a = 1/2
---
Solve for "b":
6a+b = -1
3+b = -1
b = -4
---
Equation:
y = (1/2)x^2-4x+6
==============
Cheers,
Stan H.
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