Question
How can I tell what direction this parabola open up
-2x^2 +16x+24y-224=0
We just started this in class today do I need to change this into another format
-2x^2 +16x+24y-224=0
We just started this in class today do I need to change this into another format
Answers
MathMate
The leading coefficient tells the story.
The leading coefficient of a polynomial is the coefficient (number) associated with the variable of the highest power, in this case, x².
If the leading coefficient (-2) is negative, it is <i>concave down</i>, i.e. it opens downwards. If the leading coefficient is positive, it is <i>concave up</i>.
An easy way to remember is the concavity follows the same direction along the y-axis as the leading coefficient. Positive => upwards, negative => downwards.
The leading coefficient of a polynomial is the coefficient (number) associated with the variable of the highest power, in this case, x².
If the leading coefficient (-2) is negative, it is <i>concave down</i>, i.e. it opens downwards. If the leading coefficient is positive, it is <i>concave up</i>.
An easy way to remember is the concavity follows the same direction along the y-axis as the leading coefficient. Positive => upwards, negative => downwards.