Solving Quadratics Review

Graphing

100

Where should you look to determine the zeros of a quadratic function?

X-intercepts

200

A quadratic function has no solutions. Draw what this could look like. 

Either a U that is entirely above the x-axis or a reflection of U that is entirely below the x-axis. 

300

Plot 3(x-4)² - 12 in your graphing calculator. Determine the solutions. 

(2,0) & (6,0)

400

Solve 2x² + 4x - 16 = 0 by graphing. 

(-4,0) & (2,0)

500

Solve the equation by graphing. 

x² + 10x + 25 = 0

(-5,0)

Factoring

100

(2x - 13)(x + 8) = 0

X = 13/2 and x = -8

200

Solve by factoring: x² + 2x - 35 = 0

(-7,0) & (5,0)

300

2x² + 9x + 10 = 0

x = -2 and x = -5/2

400

2x² + 3x + 8 = x² + 48

x = -8 and x = 5

500

3x² + 4x - 7 = -x² - 8x

x = -7/2 and x = 1/2

Quadratic formula

100

Find the discriminant of the quadratic with a=5 b=8 and c=2

B²-4AC = 8²-4(5)(2) = 44

200

determine a,b,&c

2x² + 9x - 5 = 3x - 17

A = 2

B = 6

C = 12

300

Simplify sqrt(147)

147 = 3*7*7 so sqrt (147) = 7sqrt(3)

400

Solve using the quadratic formula:

x² + 8x + 1 = 0

x = [-8 +- sqrt(60) ] / 2

x = [-8 +- 2sqrt(15) ] / 2 

x = -4 +- sqrt(15)

500

Solve using quadratic formula:

x² + 9x - 1 = 3x + 12

A = 1   B = 6   C = -13

x = [ -6 +- sqrt (88) ] / 2

x = -3 +- sqrt (22)

Taking square roots

100

2x² = 200

x = 10 and -10

200

(x-3)² + 9 = 25

x = 7 or -1

300

2x² + 19 = 29

x = +- sqrt (5)

400

4(x - 1)² = 24

x = 1 +- sqrt (6)

500

(3x + 1)² - 7 = 176

x = 4 and -14/3

Characteristics

100

Does 2x² - 9x + 8 have a maximum or a minimum? How do you know?

Minimum because the parabola opens up

200

Find the vertex of 5(x + 19)² + 17

(-19, 17)

300

Find the interval of increase for

 3(x - 1)² + 7

(1, positive infinity) the graph opens up. Label negative infinity U positive infinity and circle the x-value of the vertex. 

400

What is the range of -2(x + 6)² + 5

y <= 5

Graph opens down with a max at y = 5

500

Find the vertex of 2x² + 16x + 37

-b/2a

(-4,5)