SOLUTION: When solving the quadratic equation x2 - 8x + 12 = 0, the solutions are x = 2 and x = 6. If you examine the quadratic function y = x2 - 8x +12, how can you use the solution of the

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: When solving the quadratic equation x2 - 8x + 12 = 0, the solutions are x = 2 and x = 6. If you examine the quadratic function y = x2 - 8x +12, how can you use the solution of the       Log On


   

Question 725933: When solving the quadratic equation x2 - 8x + 12 = 0, the solutions are x = 2 and x = 6. If you examine the quadratic function y = x2 - 8x +12, how can you use the solution of the corresponding quadratic equation to determine the x-intercepts of the quadratic function?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The x-intercepts are the points where the parabola (the graph of the quadratic function) crosses the x-axis.
The x-axis has the equation y=0, so the x-intercepts have y=0 .
You would just have to find their x coordinates by solving the equation
0=x2+-+8x+%2B+12 <--> x2+-+8x+%2B+12+=+0 ,
but you already know that the solutions are x=2 and x=6.

Extra:
You know that the function y=x2+-+8x+%2B+12 represents a parabola with a vertical axis of symmetry.
The x-intercepts (2,0) and (6,0) are symmetrical with respect to the vertical line that is the axis of symmetry.
The axis of symmetry passes through the midpoint of the segment connecting those x-intercepts, the point (4,0), with
x=%282%2B6%29%2F2=4 .
The equation of the axis of symmetry is x=4 .