Alvin Pugh

2022-01-23

How do you know if $y=16-4{x}^{2}$ pens up or down?

primenamaqm

Expert

Step 1
All you need to know in the orientation of a parabola is to check the $a{x}^{2}$ term.
What determines how a quadratic opens is that a value. The smaller the value, the wider the parabola, but the larger the value, the skinnier the parabola.
Low values indicate small increases, large values indicate steep and large increases. Self explanatory.
Referring to this term: $a{x}^{2}$
If $a>0$ then the parabola would open upwards.
If $a<0$ then the parabola would open downwards.
And if $a=0$ then there would be no parabola.
If $y=16-4{x}^{2}$ was rewritten to $y=-4{x}^{2}+16$. It can be easily visible that this particular parabola opens downward.

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