Quadratics Review

Solve by factoring or using quadratic formula

100

n²+8n= -15

-5, -3

200

5r² - 44r + 120 = -30 + 11r

6, 5

300

7k² - 6k = 0

6/7, 0

400

35k² - 22k + 7 = 4

1/5, 3/7

500

8x² + 21 = -59x

-3/8, -7

Complete the Square and State the Transformations

100

p² + 14p - 38

(p + 7)² + 11

Shift 7 units left and 11 units up

200

-a² - 20a - 51

-(a + 10)² + 49

Reflect across the x - axis

Shift 10 units left and 49 units up

300

2a² - 8a + 6

2(a - 2)² - 2

Vertically strectched by a factor of 2

Shift 2 units right and 2 units down

400

4n² + 4n + 36

4 (n + 0.5)² + 35

Vertically stretched by a factor of 4

Shift 0.5 units left and 35 units up

500

-6x² - 12x - 60

- 6(x + 1)² - 54

Vertically stretched by a factor of 6

Reflect in the x -axis

Shift 1 unit left and 54 units down

List the Key Features

100

Vertex, AOS, Zeroes, Y-int, Min/Max

y = x²

Vertex = (0,0)

AOS x = 0

Zeroes = 0

Y-int = 0

Min = 0

200

Vertex, AOS, Zeroes, Y-int, Min/Max

y = (x-5)² + 3

Vertex = (5,3)

AOS x = 5

Zeroes = none

Y-int = 28

Min = 3

300

Vertex, AOS, Zeroes, Y-int, Min/Max

y = -(x+3)² + 9

Vertex = (-3,9)

AOS x = -3

Zeroes = -6, 0

Y-int = 0

Max = 9

400

Vertex, AOS, Zeroes, Y-int, Min/Max

y = x² + 6x + 8

Vertex = (-3,-1)

AOS x = -3

Zeroes = -4, -2

Y-int = 8

Min = -1

500

Vertex, AOS, Zeroes, Y-int, Min/Max

y = -3x² + 6x + 8

Vertex = (1,11)

AOS x = 1

Zeroes = -0.915, 2.915

Y-int = 8

Max = 11

What is the Equation of the graph

100

Vertex at origin

Passes through the point (1, -8)

y = -8x²

200

Vertex (8,-1)

Y-intercept -17

y = -0.25(x - 8)² - 1

300

Roots at -4, 7

y intercept 56

y = -2(x+4)(x-7)

400

Roots 2, 3

Y intercept -2

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

500

Vertex (4, -16.2)

Roots -2, 10

y = 0.45 (x-10)(x+2)

Value of Discriminant and number of solutions?

100

6p²-2p-3=0

76

2 roots

200

r² + 5r + 2 = 0

17

2 roots

300

-2x² - 8x - 14 = -6

0

one root

400

9n² - 3n - 8 = -10

-63

no real roots

500

9m² + 6m +6 =5

0

one solution