If the parabola has y = -4 at both x = 2 and x = 3, then since a parabola is symmetric, its axis of symmetry must be between x = 2 and x = 3, or at x = 5/2. Our general equation can then be:
y = a(x - 5/2)^2 + k
Substitute (1, -2): -2 = a(-3/2)^2 + k
-2 = 9a/4 + k
Substitute (2, -4): -4 = a(-1/2)^2 + k
-4 = a/4 + k
Subtracting: 2 = 2a, so a = 1. Substituting back gives k = -17/4.
So the equation is y = (x - 5/2)^2 - 17/4
Expanding: y = x^2 - 5x + 25/4 - 17/4
y = x^2 - 5x + 2 (This is the standard form.)
A. Diagonals bisect each other is always true. Each diagonal<span> cuts the </span>other<span> into two equal parts. It is because of the parallel lines in the parallelogram. </span>
The basic angle for 1/2 is 60°, and cosines are negative in the first and third quadrant.
So, you take 180° - 60° = 120° to get the angle in the first quadrant, and 180° + 60° = 240° to get the angle in the third quadrant.
Since only 120° is an option, the answer is
B.
Slope 1/7 ; easiest way to remember is rise over run
