ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos

CAHSEE Math 4.2 Algebra and Functions 233 Views


Share It!


Description:

Algebra and Functions: Drill 4, problem 2. If the function for the area of a circle with respect to its diameter was graphed in the first quadrant the graph would look like which of the following?

Language:
English Language

Transcript

00:03

Okay and here's your shmoop du jour. It's all about graphs.

00:07

If the function for the area of a circle with respect to its diameter was graphed in the

00:12

first quadrant... ...the graph would look like which of the following?

00:18

Here are the potential answers...

00:20

And hit pause, try it yourself, go on.

00:25

First of all, we know that the equation for the area of a circle is pi times radius squared.

00:31

Except the question is asking for the area of a circle with respect to its diameter,

00:36

not radius.

00:42

We know that the diameter of a circle is twice the radius, or d = 2r, and so the radius

00:49

equals the diameter over 2.   Substituting d over 2 into the equation, we

00:53

see that the area equals pi times d over 2 squared...

00:57

...which equals pi over 4 times d squared. Finally, our area equation is in terms of d.

01:05

We can convert pi over 4 into decimal format... which is roughly .8d-squared.

01:11

Notice that this equation is a parabola and because the leading coefficient... the .8...

01:17

is positive, it opens upwards. Looks like (C) and (D) won't work.

01:21

The only difference between A and B is where they intersect the y-axis.

01:26

Logically, if the diameter of a circle is 0, its area must also be 0 since... there

01:31

wouldn't have been a circle in this case.

01:35

This implies that the graph must go through the origin.

01:39

Why you ask? Because the origin is the point (0,0), and on our graph, which has axies d and a.

01:46

If d is 0, a is 0, and therefore must hit the point (0, 0). That's how the origin works. Only the graph of A does.

01:55

Looks like our answer is A!

01:57

We should vamoose before things get ugly...

Up Next

CAHSEE Math 5.3 Algebra and Functions
2032 Views

CAHSEE Math: Algebra and Functions Drill 5, Problem 3. Solve the equation.

Related Videos

Simplifying Radicals
9737 Views

We don't like knocking people down to size, but we do like simplifying radicals. Join us?

Arithmetic Math
2248 Views

If fleeing criminals always fled the scene of the crime at perfect right angles, it would be much easier to determine their whereabouts. Fortunatel...

Basics of Game Theory
882 Views

Okay, so this probably isn't going to help you master Pokemon Go, but game theory can be applied to all sorts of situations. Even stomping your old...