Quadratic Functions

Discriminant

100

What is the discriminant of 

3x²-4x+3=0?

16-4(3)(3)

16-36

-20

200

What do you know about the roots of a quadratic equation if the discriminant is 0?

Real, Rational, Equal (Double root)

300

If the discriminant is -25, what do you know about the roots?

Imaginary conjugates

400

Find the discriminant and describe the roots:

5x²+10x-2=0

100-4(5)(-2)

100+40

140, real, irrational, unequal

500

Find the discriminant and describe the roots.

x^2 +2sqrt5x+1=0

20-4(1)(1)=16

Real, unequal, irrational

(not all coefficients are rational!)

Solving- Sq. roots and completing square

100

Solve 

(x+8)^2=20

x=-8+-2sqrt5

200

x^2+14x+49=5

(x+7)^2=5

x=-7+- sqrt5

300

Solve 

x^2+10x+6=0

x²+10x=-6

x²+10x+25=-6 +25

(x+5)²=19

x=-5+- sqrt19

400

Solve

2x^2 +8x+5=0

x^2+4x=-5/2

x^2+4x+4=-5/2 +8/2

(x+2)^2=3/2

x=-2+- sqrt6/2

500

Solve:

3x^2+9x+4=0

x^2+3x=-4/3

(x+3/2)^2=11/12

x=-3/2 +- sqrt33/11

Graphing- vertex form

100

State the vertex

y-5=2(x+9)^2

(-9, 5)

200

Find the y-intercept

y+7=1/2(x-4)^2

(0, 1)

300

Find the x-intercepts

y+7=1/2 (x-4)^2

4+-sqrt14

400

List domain, range, maximum or minimum value, and y-intercept.

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

D: All real numbers. 

R: 

y>=-2

Minimum value at -2

y-int: 3 1/3

500

List 5 points on the graph of

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

(-1, 3), (0,1), (-2,1) 

(0,.225), (-2,-2.225),

(1,5), (-3,5)

Solving: quadratic formula & substitution

100

Solve using the quadratic formula:

x^2+6x+4=0

-3+-sqrt5

200

Solve using the quadratic formula:

6x^2+5x+3=0

(-5+-isqrt47)/12

300

Solve using the quadratic formula:

10x^2-8x-6=-3

(4+-sqrt46)/10

400

Solve using substitution:

(2x+5)^2-3(2x+5)-4=0

z = 4, -1

x = -1/2 , -3

500

Solve using substitution.

6x-14sqrtx-12=0

z=-2/3 or 3

x=9

Graphing- quadratic form

100

What is the y-intercept of

f(x)=7x^2 +16x-23

-23

200

What is the vertex of

f(x)=x^2+8x-5

(-4, -21)

300

Find the x-intercepts of

f(x)=2x^2+10x+5

(-5+-sqrt15)/2

400

Determine if f has a maximum or minimum value then find it.

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

minimum value at -5/2

vertex (3/2, -5/2)

500

Transform the following function into vertex form, then state the vertex.

f(x)=2x^2-8x+3

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