The vertex form of the equation of a parabola is y=(x+3)^2+53 What is the standard form of the equation.

The standard form of the parabola y = x² + 6x + 62

Step-by-step explanation:

Explanation

Given that the parabola equation in vertex form

       y = ( x+3)² + 53

      y = x² + 6 x + 9 +53

     y = x² + 6x + 62

The standard form of the parabola y = a x ² + b x + c

The standard form of the parabola y = x² + 6x + 62

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.