Quadratic Functions 2

Complete the square (don't solve)

100

x^2+4x=0

(x+2)^2=4

200

x^2-2x=0

(x-1)^2=1

300

3x^2-18x+17=0

(x-3)^2=10/3

400

f(x)=x^2-6x+8

f(x)=(x-3)^2-1

500

f(x)=-2x^2-20x-11

f(x)=-2(x+5)^2+39

Solve by any method, simplify

100

x^2 – 12x – 13 = 0

x=-1, 13

200

x^2 + 8x + 5=0

x=+-sqrt(11)-4

300

x^2 – 20x + 32=-x^2

x=2, 8

400

2x^2 + 14x – 31=x^2+20

x=-17, 3

500

2x^2 – 7x – 8=-2

x=(7+-sqrt(97))/4

Number of real zeroes

100

f(x)=-7x^2+8x+2

2

200

f(x)=25x^2-10x+1

1

300

f(x)=x^2 + 10x + 25

1

400

f(x)=4x^2 – 3x + 2

0

500

f(x)=5x^2 – 3x + 1

0

Features of quadratic functions

100

Find the vertex:

f(x) = (x – 5)^2 – 16

(5, -16)

200

Find the y-intercept:

g(x) = x^2 – 6x + 8

(0, 8)

300

Find the x-intercepts:

f(x) = 2(x + 1)(x + 3)

(-1, 0), (-3, 0)

400

Find the x-intercepts:

g(x) = x^2 + 2x – 15

(-5, 0), (3, 0)

500

Find the vertex:

f(x)=x^2 + 10x – 11

(-5, -36)

Transformations

100

g(x) is f(x)=x^2 translated 6 units up. What is g(x)?

g(x)=x^2+6

200

g(x) is f(x)=x^2  translated 10 units to the right. What is g(x)?

g(x)=(x-10)^2

300

g(x) is f(x)=x^2 translated 4 units down and 3 units left. What is g(x)?

g(x)=(x+3)^2-4

400

g(x) is f(x)=x^2 reflected over the x-axis and at half the growth rate. What is g(x)?

g(x)=-1/2x^2

500

g(x) is f(x)=x^2 at thrice the growth rate and translated 6 units right. What is g(x)?

g(x)=3(x-6)^2