direction of opening y – intercept vertex aos min/max value number of solutions solutions ...

Direction of OpeningY – interceptVertexAOSMin/Max ValueNumber of solutionsSolutionsDomain and RangeIncreasing Decreasing

QUIZ REVIEW

QUIZ REVIEW

On the Calculator:- Min/Max (Vertex)- AOS- Zeros

**Put equation in y1**Hit 2nd Trace**Follow directions on

Calculator

ON THE CALCULATOR

September 26 th

PROPERTIES OF QUADRATIC

EQUATIONS - EQUATION

y = ax2 + bx + ca ≠ 0

STANDARD FORM OF QUADRATIC EQUATIONS

Let’s look at y = x2 and y = -x2:

Think-Pair-Share:What do you notice about these two graphs? What is the difference between the two equations? What do you think the difference means?

Parabola

WHAT DOES THE EQUATION OF A QUADRATIC FUNCTION

TELL US?

Direction of opening: If a>0, the direction of opening is UP.

If a<0, the direction of opening is DOWN.

Example: y = 5x2 + 10x – 7

WHAT DOES THE EQUATION OF A QUADRATIC FUNCTION

TELL US?

Graph the equation in you calculator:

y = x2 + 4x – 5

What is the y – intercept?

WHAT DOES THE EQUATION OF A QUADRATIC FUNCTION

TELL US?

y – intercept:In standard form, c gives us the y-intercept:

y = ax2 + bx + c

Example: y = 5x2 + 10x – 7

WHAT DOES THE EQUATION OF A QUADRATIC FUNCTION

TELL US?

1. y = -8x2 + 2x + 1

2. y = 6x2 – 24x - 4

WHAT IS THE DIRECTION OF OPENING AND Y – INTERCEPT OF

THE EQUATIONS?

Axis of Symmetry (AOS): we can use the formula to find the AOS.

Example: y = -x2 + 8x + 16

WHAT DOES THE EQUATION OF A QUADRATIC FUNCTION

TELL US?

Vertex: plug the AOS in for x and find the y value of the vertex.

Example: y = -x2 + 8x + 16

WHAT DOES THE EQUATION OF A QUADRATIC FUNCTION

TELL US?

y = -8x2 + 2x + 1 y = 6x2 – 24x - 4

FIND THE AOS AND VERTEX

Maximum/Minimum: highest/lowest point- If a < 0, the graph has a ______________- If a > 0, the graph has a ______________

The maximum/minimum value is the y – value of the vertex.

Example: y = -x2 + 8x + 16

WHAT DOES THE EQUATION OF A QUADRATIC FUNCTION

TELL US?

1. y = x2 + 6x + 8Direction of Opening:y – intercept:AOS:Vertex:Max or Min Value:

PROPERTIES – PRACTICE USING THE EQUATION

-x2 + 10x + 25 2x2 – 4x – 6 For the two quadratics answer these questions:

1. Direction of Opening?2. Y – intercept?3. AOS?4. Vertex?

WARM UP

y = -2x2 + 12x + 16Direction of Opening:y – intercept:AOS:Vertex:Max or Min Value:Sketch the Graph:

PROPERTIES – REVIEW USING THE EQUATION

y = 2x2 + 24x + 20Direction of Opening:y – intercept:AOS:Vertex:Max or Min Value:Sketch the Graph:

PROPERTIES – REVIEW USING THE EQUATION

You and your partner will either have a picture of a graph or the equation of the graph. You should take a couple minutes to right down everything you know about

your graph/equation. Then when I say, walk around the room and find the pair

with the matching graph/equation.

Example: Matching Graph to Equation

ACTIVITY

FLEX - FACTORING REVIEW

Factor the following expressions:1. x2 – 15x + 50: (x – 5)(x – 10)2. 12xy – 4y + 9x – 3: (4y + 3)(3x – 1)3. x2y - 3x2 – 8y - 24: (x2 – 8)(y – 3)4. x2 – 36: (x – 6)(x + 6)5. 20x2 – 16x: 4x(5x – 4)6. 4x2 - 24x + 36: 4(x – 3)(x – 3)7. 2x3 + 12x2 + 16x: 2x(x + 4)(x + 2)8. x2 - 5x - 14: (x – 7)(x + 2)9. 15ab – 5b + 9a – 3: (5b – 3)(3a – 1)

Remember: factor the equation then set each set of parentheses equal to 0 and solve for x.

Example (solve by factoring): y = 3x2 + 2x – 5

ZEROS, ROOTS, X – INTERCEPTS, SOLUTIONS

(x + 5)(x – 1) = 0

(2y – 1)(3y + 2) = 0

(3x – 3)(4x – 8) = 0

(7n – 14)(6n – 3) = 0

YOU TRY

1. y = x2 - 10x - 11 2. y = -3x2 + 12

SOLVE BY FACTORING

3. y = -2x2 + 6x + 56 4. y = 4x2 - 8x - 32

SOLVE BY FACTORING

5. y = 3x2 – 9x 6. y = 3x2 + 4x – 4

SOLVE BY FACTORING

Complete All Stations – Due at the end of class time!

STATIONS REVIEW

Worksheet

HOMEWORK