SOLUTION: Give an example of a quadratic equation with a double root, and state the relationship between the double root and the graph of the related function.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Give an example of a quadratic equation with a double root, and state the relationship between the double root and the graph of the related function.      Log On


   

Question 1029328: Give an example of a quadratic equation with a double root, and state the relationship between the double root and the graph of the related function.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=a%28x-h%29%5E2%2Bk

You could find the roots according to y=0 and there may be 0, or 1, or 2 roots (real ones). Vertex is (h,k).

Let k=0 in that standard form equation.
y=a%28x-h%29%5E2
You can solve to find the roots;
a%28x-h%29%5E2=y
%28x-h%29%5E2=y%2Fa
x-h=0%2B-+sqrt%28y%2Fa%29
If y=0, then the solution here for x is the "roots";
x=h%2B-+sqrt%28y%2Fa%29
x=h%2B-+sqrt%280%2Fa%29
x=h%2B-+0
highlight%28x=h%29, which is only ONE root. The vertex and the x-intercept will be the same value. The graph touches the x-axis at exactly one point.

This is generalized, and not a specific example.