The shape of a quartic with a negative leading coefficient most closely resembles what letter

M

Step-by-step explanation:

A quartic equation/function is a fourth degree polynomial. The general form is:

We can put any values for the variables a, b, c, d, and e.

The general shape of a fourth degree polynomial is in the shape of the English letter "W".

The leading coefficient is the value of "a".

If a is negative, the curve gets upside down, so a "W" going upside down would resemble an "M".

A graph of a quartic with negative leading coefficient is shown attached. The equation is:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15