Question

Respond to the following question with either a TRUE or FALSE: "The following parabola opens down: f (x) = -x2 + 5"

O TRUE because the leading coefficient is negative.
O TRUE because the linear function is negative.
O FALSE because the 5 is.positive.
O FALSE because this function is actually linear and not a parabola.
O I'm not sure how to approach this problem...yet.

Answer 1

Answer: A) True because the leading coefficient is negative

Step-by-step explanation:

The leading term is -x^2 since this term has the largest exponent.

The leading coefficient is -1 as it's the coefficient of the leading term.

It might help to write -x^2 as -1x^2

The negative leading coefficient makes the parabola open downward, so each endpoint goes off to negative infinity. The graph looks like a frowny face. You can think of a negative emotion going with a frowny face, so that negative emotion matches with the negative leading coefficient. There are probably other ways to remember but that's the trick I use.