Question

NO LINKS!!! For each below, tell whether the table represents a linear, exponential, inverse or no relationship. Write an equation for each table (if possible).​

Answer 1

Exponential

It should be a parabola

The best shortcut trick is the fact about the parabola is that parabola is symmetric and axis of symmetry goes through vertex

So on both sides of vertex i e same distance on x from vertex the two x values have same y value .

Observe the table and find similar y values

• (0,0) and (4,0)
• (1,-3) and (3,-3)

FIND midpoint of x which is axis of symmetry

• 0+4/2=2
• 1+3/2=2

We have been sured axis of symmetry is at x=2

• Vertex (2,-4)

Form equation

• y=a(x-h)²+k
• y=a(x-2)²-4

Put (5,5)

• 5=a(5-2)²-4
• 5=a(3²)-4
• 9a-4=5
• 9a=9
• a=9

Final equation

• y=(x-2)²-4

Answer 2

`\large \boxed{\sf y = (x - 2)^2 - 4}`

`\large \boxed{\sf Quadratic \ Function}`

Step-by-step explanation:

A linear function shall increase linearly. Here due to mass differences between points, it is visible that it is not a linear function.

There is a better way to understand what type of equation it is after plotting the coordinates on the graph.

Look at the attachment!

After looking so, we can determine this as quadratic function.

** Not a exponential, inverse, linear function **

To find equation:

Quadratic function: y = a(x - h)² + k

Locate (h, k) = (2, -4)

Take any other suitable point for example = (0, 0)

Insert values to find (a),

a(0 - 2)² - 4 = 0

4a = 4

a = 1

Now Join together: y = 1(x - 2)² - 4 --- Quadratic Equation