Aparabola with vertex (1,5) and y-intercept
(0,2) crosses the x-axis in two places. one x-
intercept is at (-0.29,0). find the other x-
intercept. separate the values with a comma.

So the other x-intercept we are looking for is (2.29 , 0).

Step-by-step explanation:

The equation for a parabola in vertex form is

where (h,k) is the vertex.

So we are given (h,k)=(1,5) so let's plug that in.  This gives us the following equation for our parabola:

.

Now we need to find . Let's find by using another point (x,y) given.  We are given that (0,2) is on our parabola. So when x is 0, y is 2.

This gives us the equation:

So our parabola in vertex form looks like this:

Now we are asked to find the x-intercepts.

You can find the x-intercepts by setting y equal to 0 and solving for x.

So let's do that:

Subtract 5 on both sides:

Divide both sides by -3:

Take the square root of both sides:

Add 1 on both sides:

So the two solutions in exact form are

Putting both into calculator (separately) gives:

So the other x-intercept we are looking for is (2.29 , 0).

add -60 to 120 which will result in : 2x+3y=180

then subtract 2x: 3y=-2x+180

lastly, divide by 2: y= -2/3x+60

hope this is the answer you're looking for: )