Which equation will produce the narrowest parabola when graphed?

A.) y = 3x²

B.) y = 0.75x²

C.) y = -6x²

D.) y = -0.75x²

A.) y = 3x²

B.) y = 0.75x²

C.) y = -6x²

D.) y = -0.75x²

A

Also, to reflect a graph over the x-axis, simply take the negative of the y-value.

Think about the parent function for quadratics, which is y = x².

- If you were to multiply the y value, which is x², by say 6. This would make the new parabola (y = 6x²) more narrow than the parent function. Then if you desired to reflect that graph over the x-axis,

it would be written as y = -6x².

To clarify from the answer choices above, the choice which contains the highest absolute value regarding the coefficient of x², would in fact be the narrowest.

**parabola is stretched away from the x-axis,**thus making it more narrow,**by multiplying the y-value by a number greater than 1**. On the other hand,**a parabola is compressed toward the x-axis**, thus making it wider,**by multiplying the y-value by a number between 0 and 1.**Also, to reflect a graph over the x-axis, simply take the negative of the y-value.

Think about the parent function for quadratics, which is y = x².

- If you were to multiply the y value, which is x², by say 6. This would make the new parabola (y = 6x²) more narrow than the parent function. Then if you desired to reflect that graph over the x-axis,

it would be written as y = -6x².

To clarify from the answer choices above, the choice which contains the highest absolute value regarding the coefficient of x², would in fact be the narrowest.

**C.) y = -6x²****Ask Algebra House**