Graph the function and identify the domain and range y=-3x^2

Domain : ( -∞ , ∞ ) ; range ( -∞ , ∞ ]

Step-by-step explanation:

Given :  y=-3x².

To find :  Identify the domain and range .

Solution : We have given that  y = -3x².

Domain :  the domain of the function is the set of input values for which function is defined .

So, the function is defined for all real values .

Notation : ( -∞ , ∞ )

Range : The set of values of dependent variable for which function is defined .

Range  for quadratic function is always less than or equal to 0 .

Notation : ( -∞ , ∞ ]

Therefore , Domain : ( -∞ , ∞ ) ; range ( -∞ , ∞ ]

it would open into a square depending on the type of envelope i’m not sure about the second part

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form