Punch in a bunch of equations look at the graph and equation

Punch in a bunch of equations, look at the graph and equations and draw some conclusions. Type in x^2 in the calculator ( desmos.come) and hit enter. This is your standard function, the square function. Now punch in each of the following equations. x^2+2   x^2+5   x^2+7   x^2-2   x^2-4     x^2-4 x^2-8 x^2-1 x^2+1      Do not punch in   y = x^2 + 2 , just punch in the x^2 +2 . Look for pattern. What is happening to each parabola??? Why ??? Draw some conclusions ?

Solution

since x^2 is the standard function, the parabola passes through point 0.

for x^2+2 according to the standard function,the parabola moves 2 positions upward.

for x^2+5 according to the standard function, the parabola moves 5 positions upward.

for x^2+7 according to the standard function, the parabola moves 7 positions upward.

for x^2-2 according to the standard function, the parabola moves 2 positions downward.

for x^2-8 according to the standard function, the parabola moves 8 positions downward.

for x^2-4 according to the standard function, the parabola moves 4 positions downward.

for x^2-1 according to the standard function,the parabola moves 1 position downward.

for x^2+1 according to the standard function, the parabola moves 1 position upward.

overall considering the parabola to be moving upwards and downwards, the parabola is finally plotted at y=-11.