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

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) (Show Source): You can put this solution on YOUR website!

a)
Factorable being a perfect square:
it shows you got X-intercept, (2,0)
Let' see the vertex to see where we are, via Vertex Form:
We complete the square of the given eqn:

The vertex exists @ (2,0)
Letting

, Y-Intercept
Conclusion, given eqn it has ONLY X-Intercept because the vertex lies on the x-axis.
As you see below;

b)
For this solution toe xist, the discriminant should not be a negative number:
By Quadratic so we can see the roots (X-intercepts):
where
Solving for the discriminant:
The dicriminant is zero. Therefore, there's only one solution.

Let

Y-intercept

Thank you,
Jojo

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