Question

pls help me!!

1. The graph of y = f(x) is a parabola whose vertex is at (1, -2). The graph of y = f(x - 3) is also a parabola. Where is the vertex of the graph of y = f(x-3)? Write your answer as an ordered pair.


2. The graph of has the line as an axis of symmetry. The graph also passes through the point. Find another point that must lie on the graph of y = f(x).


3. The graph of y = f(x) is shown in the first picture in red. Find the equation that corresponds to the blue graph.

Enter your answer in the form "y = …".


4. The graph of y = h(x) is shown in red in the second picture. Compute h(h(7)).

(Assume grid lines are spaced 1 unit apart.)


5. In the third picture is a portion of the graph of a function, y=u(x):

What is the exact value of u(-2.72)+u(-0.81)+u(0.81)+u(2.72)?

Answer 1

Answer:

Q1

The graph of y = f(x), has vertex at (1, -2)

The vertex of a function f(x - 3) is going to be:

• (1 - 3, -2) = (-2, -2)

Q2

• The graph of y = f(x) has the line x = 5 as an axis of symmetry. The graph also passes through the point (8,-7). Find another point that must lie on the graph of y = f(x).

The axis of symmetry is at the same distance from the symmetric points.

x = 5 is a vertical line. The point (8, -7) is 3 units to the right. So the mirror point will be 3 units to the left and have same y-coordinate: x = 5 - 3 = 2

The point is (2, -7)

Q3

The graph in blue is the translation of the red to the left by 2 units.

So the equation is:

• y = f(x + 2)

Q4

y = h(x) is graphed

• h(7) = 5
• h(h(7)) = h(5) = -1

Q5

The graph of the function y = u(x) given

This is a odd function.

The coordinates of u(x) and u(-x) add to zero because u(-x) = -u(x)

Therefore:

• u(-2.72) + u(-0.81) + u(0.81) + u(2.72) =
• [u(-2.72) + u(2.72)] + [u(-0.81) + u(0.81)] =
• 0 + 0 = 0