Graph a triangle (ABC) and reflect it over the x-axis to create triangle A'B'C'. Describe the transformation using words. Make sure you refer to the characteristics and the coordinates. Draw a line segment from point A to the reflecting line, and then draw a line segment from point A' to the reflecting line. What do you notice about the two line segments you drew? Do you think you would see the same characteristic if you drew the line segment connecting B with the reflecting line and then B' with the reflecting line? How do you know? (10 points)

See below.

Step-by-step explanation:

This is analagous to reflecting  an object if a mirror. The virtual image appears to be the same distance behind the mirror as the object is in front of it.

So the line drawn from  point A to the x-axis will be equal in length to the line drawn for point A' to the x-axis. If the coordinates of x are, say, (2, 3) then the coordinates of A' will be ( 2, -3)   .Note the x coordinate  does not change but the y coordinate becomes negative.

You would see the same thing with B and B' because it is a reflection. The distances between the corresponding points on the 2 triangles will be equal.

x² + 3x + 7 = 0       [ax² + bx + c]

a = 1

b = 3

c = 7

quadratic formula:

    (+/- is this ±)

plug in the numbers into the variables

your answer is a