Question

What are the X and Y intercepts of y= -2(x-4)2 +3

Answer 1

Answer: x-intercepts are ( 2.775,0) and (5.225,0)

And y-intercept is (0,-29)

Explanation:

Here the given equation is,

`y = -2(x-4)^2+3`

For x-intercept, y = 0,

Put y = 0 in the above equation of parabola,

We get,
`-2(x-4)^2 + 3 = 0`

`-2(x^2+16+8x) + 3 = 0`

`-2x^2-32-16x + 3 = 0`

`-2x^2-16x -29 = 0`

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)