The first equation also has a minimum because it opens upwards (meaning it keeps going on and on forever in the upwards direction from its vertex). The second one has a maximum because it opens downwards (meaning it keeps going on and on forever in the downwards direction away from its vertex)Hope this helped!......
The direction each parabola opens
The vertex of each parabola
y = x2 − 2x
y = −2x2 + 4x − 3
Q1: Both answers A and B because they both are negative, meaning that they both open downwards. Because of this, they both have vertexes that are the highest point of the parabola.
Q2: All you have to do is factor the equation. Because they are not factorable without using complex numbers, this means that it doesn't cross the X axis. This automatically out-rules the last two. The first one is out ruled because if you input the x coordinate, it doesn't equal 50 (y coordinate).
Q3: (x − 3)(4x + 2) factor them out and you get y=4x2+2x-12x-6 or y=4x2-10x-6 the b term is -6
Q4: Both the second and the fourth equations open downwards because they have a negative in front of the leading term. Easy as that.
Q5: There is no graph provided
Q6: Always! The x squared term is what makes it a parabola and not another function. Even if the equation is y=X2 for instance. The x2 is the x-squared term. the x term is not present, meaning that it is 0x. The constant term is also 0 because it isn't there either. The true equation (with all terms included) would be y=x2+0x+0
Q7: The first equation opens upwards because the leading term is positive as opposed to the second which is negative. The first equation also has a minimum because it opens upwards (meaning it keeps going on and on forever in the upwards direction from it's vertex). The second one has a maximum because it opens downwards (meaning it keeps going on and on forever in the downwards direction away from it's vertex)
Hope this helped!
