Question

How is the graph of the parent quadratic function transformed to produce the graph of y=-(2x+6)^2+ 3?

Answer 1

Answer:

The graph is compressed horizontally by a factor of 2, shifted left 3, reflected over the x-axis, and translated up 3.

 because we have 2x in the parentheses  ( 2x + 6)  = 2(x + 3)

Step-by-step explanation:

Answer 2

Answer:

An oblonger parabola translated left, rotated down and shifted up

Step-by-step explanation:

1) The parent function of $y=-(2x+6)^{2} +3$ is $y=x^{2}$ since it preserves its basic characteristics of a quadratic function and it is the simplest quadratic function, then it is a fair to say that.

2) Looking at the graph below $y=-(2x+6)^{2} +3$, this is a geometric transformation of $y=x^2$

When we do $y= -(2x+6)^2$, we oblong the parabola two times, translate it to left due to its addend +6 and rotate it down since there is a negative sign.

Finally, by adding +6 we shift it up.

Check the graph below, please.