What is the vertex of the graph of y = x2 + 4x-1

vertex = (- 2, - 5 )

Step-by-step explanation:

Given a quadratic in standard form , y = ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

= -

y = x² + 4x - 1 ← is in standard form

with a = 1 and b = 4, thus

= - = - 2

Substitute x = - 2 into y for corresponding value

y = (- 2)² + 4(- 2) - 1 = 4 - 8 - 1 = - 5

vertex = (- 2, - 5 )

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