Answer: x-intercepts are ( 2.775,0) and (5.225,0)
And y-intercept is (0,-29)
Step-by-step explanation:
Here the given equation is,
[tex]y = -2(x-4)^2+3[/tex]
For x-intercept, y = 0,
Put y = 0 in the above equation of parabola,
We get, [tex]-2(x-4)^2 + 3 = 0[/tex]
[tex]-2(x^2+16+8x) + 3 = 0[/tex]
[tex]-2x^2-32-16x + 3 = 0[/tex]
[tex]-2x^2-16x -29 = 0[/tex]
By solving this equation,
We get, x = 2.775 or x = 5.225
Therefore, x-intercept of the given parabola are (2.775, 0) and (5.225,0)
Now, for y-intercept, x = 0
By putting x = 0 in the given equation of parabola,
We get, y = -29
Thus, y-intercept of the given parabola = (0,-29)
