Solving for the x-intercepts of a Parabola given the Equation
Answer:
[tex]x = 3[/tex] and [tex]x = 1[/tex]
Step-by-step explanation:
[tex]x[/tex]-intercepts are just the values [tex]x[/tex] when [tex]y = 0[/tex].
Solving for [tex]x[/tex]:
[tex]0 = -4(x -2)^2 +4 \\ -4(x -2)^2 +4 = 0 \\ -4(x -2)^2 = -4 \\ 4(x -2)^2 = 4 \\ (x-2)^2 = \frac{4}{4} \\ (x -2)^2 = 1 \\ x-2 = \pm \sqrt1 \\ x -2 = \pm 1 \\ x = \pm 1 +2[/tex]
Solving for the Positive Square Root:
[tex]x = 1 +2 \\ x = 3[/tex]
Solving for the Negative Square Root:
[tex]x = -1 +2 \\ x = 1[/tex]
