## Pre-AP Algebra 2 Spring 2017 ProjectB8

By: ALYSSA MATHEW and LIANA DISI

### Equation #1: Real Solution

#### f(x)=x²+10x+16

GRAPH:

TABLE:

FACTORING:

X=-2 and x=-8

COMPLETING THE SQAURE:

X=-2 AND X=-8

QUADRATIC FORMULA:

X=-2 AND X=-8

AXIS OF SYMMETRY:

X=-5

VERTEX FORM:

F(x)=(x+5)²-9

Y-INTERCEPT:

Y-INTERCEPT= (0,16)

TRANSFORMATION:

G(x)=-1(x-3)²+17

### Equation #2: Nonreal solution

#### F(x)=x²+4x+5

GRAPH:

COMPLETING THE SQUARE:

x=-2±i

QUADRATIC FORMULA:

X=-2±I

AXIS OF SYMMETRY:

X=-2

VERTEX:

(-2,1)

Y-INTERCEPT:

Y-INTERCEPT= (0,5)

DISCRIMINANT:

discriminant=2i

VERTEX FORM:

F(x)=(X+2)²+1

TRANSFORMATION:

G(x)=(x+4)²-6

### EquaTion #3: story problem

#### x=1/2y²-6y+18

During an earthquake, a McDonald's sign split in half vertically and the half that broke off fell into a crack in the ground. To determine how much of the sign they need to pull out, the contractors need to find the point where the half broken McDonald's sign hits, or enters the ground, the vertex point of how high the sign is off of the ground, the focus point and directrix of the sign and the symmetry line that cuts the broken sign in half. The equation that represents this situation is x=1/2y²-6y+18. Find the important information.

(this photo was photoshopped by us it is our picture)

GRAPH:

Y-INTERCEPT/VERTEX:

Y-INTERCEPT/VERTEX= (0,6)

X-INTERCEPT:

SOLUTION= (18,0)

FOCUS:

F(1/2,6)

DIRETRIX:

X= -1/2

AXIS OF SYMMETRY:

Y=6

Credits:

Created with images by Pixapopz - "math blackboard education" • Snufkin - "mathematics count science"

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