SOLUTION: Find the x-intercepts of the graph and compare them with the solutions of the corresponding quadratic equation y=x^2-9x+18.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the x-intercepts of the graph and compare them with the solutions of the corresponding quadratic equation y=x^2-9x+18.       Log On


   

Question 448483: Find the x-intercepts of the graph and compare them with the solutions of the corresponding quadratic equation y=x^2-9x+18.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

y=x^2-9x+18

Note: the vertex form of a parabola, y=a%28x-h%29%5E2+%2Bk where(h,k) is the vertex

y=x^2-9x +18   |Completing the square

y = [(x-4.5)^2 - 20.25] +18

y = (x-4.5)^2 - 2.25   Vertex(4.5,-2.25) a = 1 > 0 parabola opens upward

x-intercepts when y = 0 are also the solutions for the quadratic equation

 (x-4.5)^2 = 2.25

    x-4.5 = ± sqrt%282.25%29

      x+=+4.5+%B1+1.5%29  x = 6 or x = 3

OR

 x^2 - 9x + 18 = 0  Using Quadratic Formula to solve for x

x+=+%28-b+%2B-+sqrt%28+9%29%29%2F%282%2Aa%29+ 

x+=+4.5+%2B-+3%2F2%29 

   x = 4.5 ± 1.5   x = 6 or x = 3