SOLUTION: Quadratic Equations Find the x-intercepts of each parabola. a) y=x^2-4x+4 b) y=4x^2-12x+9

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Quadratic Equations Find the x-intercepts of each parabola. a) y=x^2-4x+4 b) y=4x^2-12x+9      Log On


   



Question 177821: Quadratic Equations
Find the x-intercepts of each parabola.
a) y=x^2-4x+4
b) y=4x^2-12x+9

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

a) y=x%5E2-4x%2B4
Factorable being a perfect square: %28x-2%29%28x-2%29=0
it shows you got X-intercept, (2,0)
Let' see the vertex to see where we are, via Vertex Form: y=a%28x-h%29%5E2%2Bk2
We complete the square of the given eqn:
%28x%5E2-4x%2B4%29%2B4-4
%28x-2%29%5E2%2B0
The vertex exists @ (2,0)
Letting f%28x%29=0
y=0%5E2-4%280%29%2B4
y=4, Y-Intercept
Conclusion, given eqn it has ONLY X-Intercept because the vertex lies on the x-axis.
As you see below;

b)y=4x%5E2-12x%2B9
For this solution toe xist, the discriminant should not be a negative number:
By Quadratic so we can see the roots (X-intercepts):
wheresystem%28a=4%2Cb=-12%2Cc=9%29
Solving for the discriminant: -b%5E2-4ac=-12%5E2-4%2A4%2A0=144-144=0
The dicriminant is zero. Therefore, there's only one solution.

x=%2812%2B-sqrt%28144-144%29%29%2F8=%2812%2B-0%29%2F8=12%2F8=highlight%281.5=x%29
Let f%28x%29=0
y=4%280%29%5E2-12%280%29%2B9
y=9 Y-intercept

Thank you,
Jojo