Algebra 2B Exam 1 Review

6.1 Graphing

100

What is quadratic form?

f(x)=ax² + bx + c

200

What is the graph of any quadratic function called? On the graph, what is the axis of symmetry, vertex, and zeros?

The graph of any quadratic function is called a parabola. The axis of symmetry is the vertical line at which the parabola is symmetric. The vertex is where the parabola and axis of symmetry intersect. Zeros are the x-coordinates where the graph intersects with the x-axis.

300

Label the quadratic term, linear term, and constant term in the equation f(x)= 4x² + 3x -5

quadratic term: 4x² 

linear term: 3x

constant term: -5

400

Solve the following equation by graphing: f(x) = x²-4x+3

*desmos*

6.2 Factoring

100

What is zero product property (according to the textbook AND in your own words)?

Textbook: For any real numbers a and b, if ab=0, then either a=0, b=0, or both.

If two things multiply to become zero, then at least one of them must equal zero.

200

Factor the following quadratic equation:

0=15x+5x²

0=15x+5x²

0=5x(3+x)

0=5x AND 3+x=0

x=0 AND x=-3

300

Solve by factoring: x²-5x+4=0

(x-1)(x-4)=0

x-1=0 -> x=1

x-4=0 -> x=4

400

Solve by factoring: x²+7x=-10

Rewrite as x²+7x+10=0

(x+2)(x+5)=0

x+2=0 -> x=-2

x+5=0 -> x=-5

6.3 Completing the Square

100

When/why would you use completing the square?

When an equation does not contain a perfect square, you can create a perfect square

200

How do you complete the square?

You take the b term, divide it by 2 (or multiply by 1/2) and then square it.

(c/2)²

300

Find the value of c that makes x²+16x+c a perfect square

x²+16x+c

16/2=8

8²=64

Answer: 64

400

Solve by completing the square: x²+6x=16

x²+6x=16

x²+6x+c=16+c

Solve for c: (6/2)²=9

x²+6x+9=16+9

(x+3)²=25

x+3=5; x+3=-5

x=2; x=-8

6.4 Quadratic Formula

100

Write the quadratic formula

*will write on the board*

200

Solve using the quadratic formula: 

x²-10x=24

x=12

x=-2

300

Solve using the quadratic formula:

x²-7x-2=0

*see teacher's edition page 354*

400

Solve using the quadratic formula:

x²-3x+7=0

*see teacher's edition page 355*

6.6 Analyzing Graphs of Quadratic Functions

100

What is the general form of a parabola equation?

y=(x-h)^2+k

200

Name the vertex and axis of symmetry for the graph of f(x)=(x+11)^2+8

Vertex: (-11, 8)

Axis of symmetry: x=-11

300

Graph f(x)=4(x+3)^2. Name the vertex, axis of symmetry, and direction of opening for the graph.

graph: *desmos*

vertex: (-3,0)

axis of symmetry: x=-3

direction of opening: up

400

Write the equation of the parabola that passes through the points at (9,-3) (6,3) and (4,27)

f(x) = 2(x-8)^2 - 5