ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos


Quadratic Equations Videos 18 videos

ACT Math 1.3 Intermediate Algebra
506 Views

ACT Math Intermediate Algebra Drill 1, Problem 3. Can you find the value of a in this expression?

CAHSEE Math 4.2 Algebra and Functions
234 Views

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 quad...

CAHSEE Math 4.3 Algebra and Functions
302 Views

Algebra and Functions: Drill 4, Problem 3. The sum of the quadratic parent function and the line given has which of the following as its graph?

See All

SAT Math 8.6 Algebra and Functions 231 Views


Share It!


Description:

SAT Math 8.6 Algebra and Functions

Language:
English Language

Transcript

00:03

It's a bird! It's a plane! It's Shmooperman...guy!

00:09

Find the positive x-coordinate of the point where the graphs of the equations…

00:14

y = -2x squared - 6 y = -3x - 8 …intersect.

00:22

Okay…so this question is asking us to solve for two linear equations.

00:28

So, back in our old algebra days, we knew we had several methods that could help us do this…

00:33

Solving by substitution…

00:35

…solving by elimination…

00:36

…or solving by graphing.

00:38

So in this case we can do any of these, but the easiest would be to just set them equal,

00:42

because…y equals y.

00:44

So we have -2x squared – 6 equals -3x – 8.

00:50

Now combine like terms and move everything to one side and we get:

00:54

2x squared – 3x – 2 = 0

00:59

…and that looks like a FACTORABLE quadratic equation.

01:03

Easiest way to solve this equation is to factor by grouping.

01:07

So if we split our -3x into x and -4x...

01:12

...we get 2x squared + x - 4x - 2 = 0.

01:19

This whole thing factors into x(2x + 1) - 2(2x + 1) = 0

01:27

Now we both have x and -2 multiplied by the quantity 2x + 1.

01:31

Do you know what we have to do next?

01:33

Factor out that 2x + 1.

01:36

Our final, fully factored equation is (2x + 1)(x-2) = 0.

01:44

Well, when x = -1/2 and 2... this equation is true.

01:48

Since the question asks for the positive x-coordinate, we'll take the positive 2.

01:54

So the answer is…2. That’s where they intersect.

Related Videos

SAT Math 9.4 Algebra and Functions
1300 Views

SAT Math 9.4 Algebra and Functions

SAT Math 9.2 Algebra and Functions
377 Views

SAT Math 9.2 Algebra and Functions

SAT Math 2.1 Geometry and Measurement
2779 Views

SAT Math 2.1 Geometry and Measurement. What is the measure of angle z in terms of x and y?

SAT Math: Identifying an Equation for the Average of Two Percentages
23 Views

In 2014, the unemployment rate of one county in California was 7%. In another county, the unemployment rate was 11%. Which of the following express...

SAT Math: Which Equation Represents Profit?
13 Views

Angela is making cookies for a bake sale. She expects each batch of her cookies to sell for $40. It costs her $10 to make one batch of cookies, and...