Find the y intercepts of 3x^2+24x-51. quadratic formula

Firstly, starting with the y-intercept. To find the y-intercept, set the x variable to zero and solve as such:

Your y-intercept is (0,-51).

Next, using our equation plug the appropriate values into the quadratic formula:

Next, solve the multiplications and exponent:

Next, solve the addition:

Now, simplify the radical using the product rule of radicals as such:

√1224 = √12 × √102 = √2 × √6 × √6 × √17 = 6 × √2 × √17 = 6√34

Next, divide:

The exact values of your x-intercepts are (-4 + √34, 0) and (-4 - √34, 0).

Now to find the approximate values, solve this twice: once with the + symbol and once with the - symbol:

The approximate values of your x-intercepts (rounded to the hundredths) are (1.83,0) and (-9.83,0).

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.