y=-3/4(x+3)squared+1

Question

How do I tell if this is a function and how do I graph this?

Answer 1

it is a function because if you pick any number for x and plug it in, you will get a value for y and only one value of y. Because the input produced only one output, y is called a function

 

You graph it the same way you graph the equation of a line.

 

Pick 5 values for x and find the value of y for each of the x values.

 

This will give you 5 points on the graph. Then you connect the dots in a smooth continuous curve which you will find is in the shape of a parabola that has a maximum and opens down.

 

Try these 5 values for x

-7

-5

-3

-1

1

 

Answer 2

Palina, 

This equation is the vertex form of a parabola. 

If you multiply out the right-hand side and simplify, you will see it in standard form: y = ax^2 + bx + c

 

But graphing this parabola is easier than that. You have it in the form y = a(x-h)^2 + k

 

Notice that the number in front of x is negative, meaning that the parabola opens (faces) down.

The vertex of the parabola is (h,k), so that's the HIGHEST point of the parabola. The vertex is (-3,+1)

Now use a T-chart to find a few more points on the parabola. (Remember that the parabola is symmetrical.)

 

If you put in x = -4 or x=-2, you will get the same y value. 

If you put in x = -5 or x = -1, those y values will be the same. 

 

Now you have enough info to graph it!