If the graph of the function y=x^2 is reflected over the x-axis , then translated two units left,write an equation to represent the function

 y = -(x + 2)²

Step-by-step explanation:

The vertex form of a quadratic equation is: y = a(bx - h)² + k    where

a: vertical stretch (if negative it is a reflection across x-axis)b: horizontal stretch (if negative it is a reflection across y-axis)h: horizontal shift (negative is left and positive is right)k: vertical shift (negative is down and positive is up)(h, k): vertex of the function

Given: reflection over x-axis → a = -1,   two units left → c = -2

Input those values into the equation:  y = -(x - (-2))²

                                              simplify:   y = -(x + 2)²

See explanation

Step-by-step explanation:

The two linear equations can be solved simultaneously;

4x+3y=8 (1)

−2x−3y=−4---(2)

If we multiply equation (1) by 1 and equation (2) by (2)

We have;

4x+3y=8 (3)

-4y - 6x = 4 ---(4)

Adding equation (3) and (4)

-3x = 12

x= -4

Substitute x = -4 into equation (1)

4(-4) + 3y = 8

-16 + 3y = 8

3y = 8 + 16

y= 24/3

y= 8

Hence;

x= -4 and y =8