2.1-2.5 Quadratics Review!

Identify Key Features

100

 What key features can you identify from the equation?y=-1/2(x-4)^2+2 

Vertex (4,2)

Opens down

Vertical compression by a factor of 1/2

200

What key features can you identify in the equation?

y=2(x+3)(x-4)

X-intercepts (-3,0) and (4,0)

Opens up

Vertical stretch by a factor of 2

300

What key features can you identify in the equation?

y=2/3(x+3)^2-1

Vertex of (-3,-1)

Opens up

Vertical compression

400

What key features can you identify in the equation?

y=2x^2 + 14x - 16

y-intercept (0,-16)

Opens up

Vertical stretch

500

What key features can you identify in the equation?

y=-3(x+1/2)^2

Vertex (-1/2,0)

Opens down

Vertical stretch

Writing Quadratic Equations From Key Features

100

Write the quadratic equation for the parabola has a vertex of (-9,8) with no vertical compression or stretch, and opens up. 

y=(x+9)^2+8

200

Write a quadratic equation for the parabola with zeros at 5 and -8, with a vertical stretch of 3 and opens up.

y=3(x-5)(x+8)

300

Write the equation of a parabola with a vertex of (-4,-2) that has a vertical compression of 1/3 and opens down. 

y=-1/3(x+4)^2-2

400

Write the equation of a parabola that has roots of -4 and 8, a vertical stretch of 2, and opens downwards.

y=-2(x+4)(x-8)

500

Write the equation of parabola that has a vertex of (2,0), a vertical compression of 1/4, and was reflected across the x-axis. 

y=-1/4(x-2)^2

Converting Equations

100

Convert the equation into STANDARD form.

y=(x-5)^2+3

y=x^2-10x+28

200

Convert the vertex form equation into STANDARD form.

y=2(x+4)^2-5

y=2x^2+16x+27

 

300

Convert the equation in FACTORED form

x^2-12x-19=-3x+17

y=(x-12)(x+3)

(x-12)(x+3)=0

400

Convert the equation into factored form.

12x^2 - 20=8x

 

y=4(x-1)(3x+5)

4(x-1)(3x+5)=0

500

Convert the vertex form equation into STANDARD form.

y=-4(x-7)^2-6

 

y=-4x^2+56x-202

GCF Factoring

100

factor using GCF

6x^3 + 7x^2

x(6x^2 + 7x)

200

Factor

25x^4+35x-15

5(5x^4+7x-3)

300

FACTOR

21x^6 -2x^4-5x^2

x^2(21x^4 -2x^2-5)

400

FACTOR

21x^6 + 7x^4+7x^3

7x^3(3x^3 + x+1)

500

FACTOR & SOLVE

36x^2+12x=-8x

4x(9x+5)=0

x=0

x=-5/9

D.O.S. Factoring

100

factor

x^2-4

(x-2)(x+2)

200

FACTOR

4x^2-9

(2x-3)(2x+3)

300

x^2-81

(x-9)(x+9)

400

FACTOR AND SOLVE

3x^2-27=0

3(x-3)(x+3)

x=-3

x=3

500

FACTOR & SOLVE

16-81x^2=0

-1(9x+4)(9x-4)

x=-4/9

x=4/9

Trinomial Factoring

100

factor

x^2 + 13x + 12

(x+12)(x+1)

200

FACTOR

x^2 − 13x + 36

(x-9)(x-4)

300

FACTOR

2x² + 14x - 16

2(x-1)(x+8)

400

FACTOR AND SOLVE

3x^2 +10x +8=0

(3x+4)(x+2)

x=-2

x=-4/3

500

  FACTOR AND SOLVE

5x^2 + 14x - 10=3x^2+6

2(x-1)(x+8)

x=1

x=-8