Math - Gr11 - chapter 3 - Quadratic Functions

Question 1

What is a quadratic function?

Answer 1

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.

Question 2

What is the graph of a quadratic function called?

Answer 2

The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in “width” or “steepness”, but they all have the same basic “U” shape.

Question 3

What is the axis of symmetry?

Answer 3

All parabolas are symmetric with respect to a line called the axis of symmetry. Formula is -b over 2a

Question 4

What is the point called where a parabola intersects its axis of symmetry?

Answer 4

Vertex

Question 5

How to graph a function video

Answer 5

https://www.youtube.com/watch?v=Cn1aFaxRyeU

Question 6

How to graph a function notes:

Answer 6

f(x) = ax^2 + bx + c
Ex. f(x) = x^2 -8x + 15
1. determine axis of symmetry x = -b over 2a
ex. x = -(-8) over 2(1) …. 8 over 2 = 4 … so the vertex is at x = 4
2. determine if graph opens up or down
ex a= 1 so a >0 so opens up
3. creates a table of values
start with the vertex and pick 2 points to one side and plug in values. This will be symmetrical on the other side of the axis of symmetry

Question 7

Determine the zeros of quadratic functions - video

Answer 7

https://www.youtube.com/watch?v=MMQ8e99l18w

Question 8

Determine the zeros of quadratic functions - notes

Answer 8

Determine the zeros of quadratic functions
Ex. x^2 -d 7x +10 = 0
1. determine if you are going to use factoring, completing the square or quadratic formula
(x - 5)(x - 2) = 0
2. solve for x
x - 5 = 0 and x - 2 = 0
x = 5 and x = 2

Question 9

Calculate the maximum or minimum values of quadratic functions - video

Answer 9

https://www.youtube.com/watch?v=Dc2_RPPk5cs

Question 10

Calculate the maximum or minimum valuesof quadratic functions - notes

Answer 10

Calculate the maximum or minimum valuesof quadratic functions
if a > 0 it opens up and vertex is a min
if a < 0 it opens down and the vertex is a max
1. To find vertx use formula - b over 2a
2. Then using x value solve the equation to find y. That is your max or min.

Question 11

Solve by completing the square

Answer 11

1. isolate the number to the other side
2. take b divide it by 2
3. rewrite equation as a square

Question 12

Solve by completing the square - video

Answer 12

https://www.brightstorm.com/math/algebra-2/quadratic-equations-and-inequalities/solving-a-quadratic-by-completing-the-square/