Question

Please help me I don't understand this at all and I can't get it. I spent 4 hours on these equations

Answer 1

Answer:

Hi. so I don't have the answers but usually if you find the name of the website your homework is from (if should be at the bottom of the page) online you can also find the answers for it. Just letting you know for this homework and future references.

Step-by-step explanation:

If the teacher asks for you to show your work the website might not show you step by step but you can just say you did it on a separate page. hope this helps!

Answer 2

Answer:

• h(x) = 1/2 |x - 1|  -  2
• h(x) = - (x + 2)²  +  3

Step-by-step explanation:

• See attached

You need to recognize the parent function by looking at the graph. Then you need to find out how different is the graph from the parent function and finally work out the equation of the graph considering the transformations.

4)

The parent function is the absolute value function:

• h(x) = |x|

Its vertex is at the origin. We see the vertex has shifted and also the slope has changed.

We can find the slope easily, the ratio of rise to run is 1/2

The function becomes:

• h(x) = 1/2 |x|

Now considering the translation. We see the vertex has coordinate of (1, -2)

It means the graph has shifted 1 unit right and 2 units down.

The shift right  is shown as:

• h(x) = 1/2 |x - 1|

and adding the shift down:

• h(x) = 1/2|x - 1| - 2

This is our final equation.

5)

Parabola is the graph of the quadratic function.

The vertex form of the function is:

• h(x) = a(x - h)² + k, where (h, k) is the vertex

Now, we see it is opening down and the vertex is at (-2, 3):

• h(x) = a(x - (-2))² + 3 = a(x + 2)² + 3

To find the value of a we can use a point on the graph. Let's use point (0, -1):

• -1 = a(0 + 2)² + 3
• -1 = 4a + 3
• 4a = -4
• a = -1

The function is:

• h(x) = - (x + 2)² + 3