Put the quadratic equation y=4x^2-24x+5 into vertex form by completing the square then state the coordinates of the vertex.

(3, -31)

Step-by-step explanation:

Factor 4 out of the first two terms:

y=4x^2-24x+5 becomes y=4(x^2 - 6x) +5

Next, complete the square of (x^2 - 6x):  It is x^2 - 6x + 9 - 9

Insert this into y=4(x^2 - 6x) +5 in place of x^2 - 6x:

y=4(x^2 - 6x) +5 => y=4(x^2 - 6x + 9 - 9) +5, or

                                y=4( (x - 3)^2 - 9 ) + 5, or

                                y = 4(x - 3)^2 - 36 + 5, or:

                                 y = 4(x - 3)^2 - 31

Compare this to:       y = a(x - h)^2 + k

We see that the coordinates of the vertex (h, k) are (3, -31), and that a = 4.

false

step-by-step explanation:

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