SOMEONE PLEASEE HELPPP

What is the change that occurs to the parent function f(x) = x^2 given the function f(x) = 2(x + 2)^2 + 1.

nikitadnepr [17]

Answer:

The graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up.

Step-by-step explanation:

The base of the quadratic function is

$f(x) = {x}^{2}$

We can transform this function to look narrower or wider.

Looking narrower is termed a stretch.

This happens when a>1

Looking wider is termed a compression.

This happens when 0<a<1

We can also

$g(x) = a {(x + h)}^{2} + k$

+h moves the parent graph to the left by h units

-h moves the parent graph to the left by h units.

+ k moves the parent function up by k units

- k moves the parent function down by k units.

The change that occurs to

$f(x) = {x}^{2}$

given

$f(x) = 2( {x + 2)}^{2} + 1$

is that, the graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up

Therefore the last choice is the correct answer.

3 0

3 years ago

the line containing the altitude to the hypotenuse of a right triangle whose vertices are p(-1, 1), q(3, 5), and r(5, -5).

finlep [7]

The equation of the straight line is given by 5y-x=6

An equation can be used to describe a straight line drawn on the Cartesian Plane. These equations have a generic structure and can change based on the slope and where the line intersects the axes.

We will greatly simplify this issue by utilizing the fact that this triangle is specified as a right triangle. We would have had to establish the presence of a right angle if it had been presented as a general triangle.

The segment QR is the hypotenuse of the triangle.

Any side's altitude is located along a line that is perpendicular to that side. We are aware that the slopes of perpendicular lines are negative reciprocals, or:

Slope of line joining Q(3, 5) and R(5, -5)

m= $\frac{y_2-y_1}{x_2-x_1}$