# How is the graph of -(x+7)^2+8 compared to the graph of f(x)= x^2?

Oct 11, 2017

The function is reflected vertically across the x-axis, it is shifted left 7 units, and it is shifted up 8 units.

#### Explanation:

$f \left(x\right) = {x}^{2}$ is the parent function and the numbers and signs we put around this function affects how the graph looks related to the parent function.

For this problem you can follow this formula:

$a {\left(x + h\right)}^{2} + k$

If $a > 1$ then it stretches the function so it’s skinnier.

If $a < 1$ then it compresses the function so it’s wider.

If $a$ is negative then it reflects the function vertically across the x-axis.

In this case $a = - 1$ so it’s not stretched or compressed, but it is reflected across the x-axis.

$h$ affects the function’s horizontal shift from the parent function

If $h$ is positive, it horizontally shifts left $h$ units

If $h$ is negative, it horizontally shifts right $h$ units

$h = 7$ so it shifts left 7 units

Finally $k$ affects the function’s vertical shift from the parent function

If $k$ is positive, it vertically shifts up $k$ units

If $k$ is negative, it vertically shifts down $k$ units

$k = 8$ so it shifts up 8 units