Step-by-step explanation:
y = 16x²
you put the x values one after the other in place of x and do the calculations.
x = -4
y = 16×(-4)² = 16×16 = 256
x = -3
y = 16×(-3)² = 16×9 = 144
x = -2.5
y = 16×(-2.5)² = 16×6.25 = 100
x = -2
y = 16×(-2)² = 16×4 = 64
x = -1.5
y = 16×(-1.5)² = 16×2.25 = 36
x = -1
y = 16×(-1)² = 16×1 = 16
x = -0.5
y = 16×(-0.5)² = 16×0.25 = 4
x = 0
y = 16×0² = 16×0 = 0
x = 0.5
y = 16×0.5² = 16×0.25 = 4
x = 1
y = 16×1² = 16×1 = 16
and so on.
36, 64, 100, 144, 256
as you can see, the y values are the same for the positive and the negative values.
because squaring a negative number is the same as squaring the same positive number. that is, because (if you remember) squaring something means to multiply that something with itself. and minus multiplied by minus is plus, as plus multiplied by plus is plus.
and that creates the symmetry around the y-axis or x = 0. everything left of the y-axis is mirrored on the right side of the y-axis (and vice versa).
