Final Exam Review 1

Final Exam Review 1

Let's start reviewing the topics you asked to cover!

First: Solve Quadratics by Factoring

• First, get equation = 0

• Then, factor with box

• Set each factor = 0

• Solve each equation!

Let's see one more

The steps are worked out on the left with the area model on the right.

An easier example

This one is already set = 0 and has a=1, so factoring is a little easier!

Multiple Choice

Solve using factoring: x²+4x-32=0

• x= -8, 4

• x= 8, -4

• x= -8, -4

Multiple Choice

Solve using factoring: x²+4x-32=0

• x= -8, 4

• x= 8, -4

• x= -8, -4

Next: Quadratic Formula

• Get = 0

• label a, b, and c

• plug into QF

• simplify as much as possible!

• Remember about imaginary solutions!!

One more

Let's see one more worked out with imaginary solutions

Remember about simplifying the radical!

Sometimes you'll get a square root you can only simplify

Questions on this?

Let's practice!

Multiple Choice

In the equation

0 = x² -5x +7, match each leading coefficient with its correct letter

• a= 0, b= 5, c= 7

• a= 1, b= -5, c= 7

• a= -7, b= 5, c= 1

• a= 1, b= 5, c= 7

Multiple Choice

Use the quadratic formula to find the solutions for

0 = 3x² + 8x - 1

• 0.1196 and -2.7862

• .7 and -16.7

• .35 and -8.35

• 0.2358 and -1.236

Multiple Choice

Use the quadratic formula to solve 2x² + 2x = 12

• -2, 3

• 2, 3

• 2, -3

• -2, -3

Next: Complete the Square

Remember: this is like factoring but it's a perfect square - the sides must match! Then we balance!

Why did we learn this again?

It's called vertex form because it shows us the vertex (maximum or minimum) of a quadratic!

Fun fact: Desmos will be your BFF!!

Did you notice my example? It showed the equation in standard form, vertex form, with overlapping graphs!! See how the blue overlapped red? It's the answer!

Multiple Choice

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

• (5, -4)

• (-5, -4)

• (-15, -4)

• (15, -4)

Multiple Choice

Complete the Square

x² + 6x = 5

• (x + 3)² = 5

• (x + 6)² = 9

• (x + 3)² = 14

• (x + 6)² = 14

Hopefully you checked with desmos!

Type in the question, then the answers. The correct answer will match!!!

Last Review Topic: TRANSFORMATIONS!

These apply to ALL equation types, and you guys did great with these - so this is just a refresher!!

Example 1

Explaining the changes from one function to another

Example 2

Remember: Desmos can help you see changes too!

Multiple Choice

What are the transformations?

y=(x-2)³+4

• Horz shift right 2 Vert shift up 4

• Horz shift left 2 Vert shift up 4

• Horz shift right 2 Vert shift down 4

• Horz shift left 2 Vert shift up 4

Multiple Choice

Describe the transformation of y = g(x) for the function

y = 3g(x - 3) + 5

• Shifted up 5 units

  Shifted right 3 units

  Stretched vertically by a factor of 3

• Shifted up 5 units

  Shifted left 3 units

  Stretched vertically by a factor of 3

• Shifted down 5 units

  Shifted left 3 units

  Stretched vertically by a factor of 3

• Shifted down 5 units

  Shifted left 3 units

  Stretched vertically by a factor of 1/3

Multiple Choice

Describe the transformation(s) that occurred from f(x)=(x-1)²+5 to g(x)=3(x+5)²-10

• Vertical stretch of 3, horizontal shift of 6 left, vertical shift down 15

• Vertical stretch of 3, horizontal shift of 6 right, vertical shift down 15

• Vertical stretch of 1/3, horizontal shift left 5, vertical shift down 10