Find function values

[kickingtoad]

Homework 2-1, problem 2

The function h(x) given in the above graph.

Enter the corresponding function value in each answer space below:

h(0)=
h(5)=
h(3)=
h(4)=

I know this is a parabola but I'm confused about how to formulate the function as in units to the right and units up.

\(\displaystyle {x{2}...}\)

 

[DrSteve]

In the expression h(x) = y , x is the x-value of the point on the graph, and y is the y-value of the point on the graph.

So, for example, since (3,2) is on the graph we have h(3) = 2

 

[mmm4444bot]

h(0) is the y-intercept.

However, the y-intercept is not shown, on this particular graph.

Perhaps, you're supposed to interpret the graph as a sloppy, quick-and-dirty graph, followed by GUESSING that h(0) is supposed to be 10.

I dunno.

For the rest of it, do you understand the given function notation? You stated difficulty "to formulate the function". I'm not sure what that means. They are not asking for a formulation, in this exercise.

Also, what does your typing "x2..." denote?

 

[kickingtoad]

Okay, I see what you're saying about finding the y value on the graph based on the x value.

I was trying to find the solutions by formulating the function from looking at the graph.

like \(\displaystyle {(x^{2}-3)+2}\)

Since -3 means three to the right, and +2 means move up two.

I'm just confused on whether the -3 or +2 goes in the brackets. I was able to get 3 correct y values with the function, except 1 came out wrong...

 

[DrSteve]

I think that you're saying that you want to write an equation for the parabola in standard form. This equation is

\(\displaystyle y = a(x-3)^2+2\) for some constant a.

We can find a by substituting in a point that we know is on the graph, like (4,3)

\(\displaystyle 3 = a(4-3)^2+2\)
\(\displaystyle 3 = a+2\)
\(\displaystyle 1 = a\)

So the equation is

\(\displaystyle y =(x-3)^2+2\)