SOLUTION: Quadratic Equations Find the x-intercepts of each parabols. c) y=x^2-4x+4 d) y=4x^2-12x+9 Thank you very much pleaseeeeeeeeeeee

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Question 178086: Quadratic Equations
Find the x-intercepts of each parabols.
c) y=x^2-4x+4
d) y=4x^2-12x+9
Thank you very much pleaseeeeeeeeeeee
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Quadratic Equations
Find the x-intercepts of each parabola.
-----------------
The x-intercepts are the points that y = 0, so set the function = 0 and solve.
c) y=x^2-4x+4
x^2 - 4x + 4 = 0
(x-2)*(x-2) = 0
Only one intercept, at (2,0)
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=0 is zero! That means that there is only one solution: .
Expression can be factored:

Again, the answer is: 2, 2. Here's your graph:

------------------
d) y=4x^2-12x+9
4x^2 - 12x + 9 = 0
(2x-3)*(2x-3) = 0
Same here, one point where the parabola is tangent to the x-axis.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=0 is zero! That means that there is only one solution: .
Expression can be factored:

Again, the answer is: 1.5, 1.5. Here's your graph:
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