Quadratics & Tangents

turning points AKA THE vertex

100

for y= (x - 5)² + 4 find and describe the turning point

(5, 4) 

so we can say the graph has shifted:

5 right, 4 up

200

for y = -(x - 4)² - 3 find:

1) turning point and describe it

2) direction of the graph 

3) y-intercept

turning point: (4,-3) maximum, 

concave down

(-3,0)

300

for y = -2(x - 2)² + 2 find:

1) turning point and describe it

2) the direction of the graph

3) x-intercepts

(2,2) turning point (maximum)

concave down

(1,0) , (3,0) x-intercepts

400

for y = x² - 12x + 20, find the:

1) turning point & describe it

2) y-intercept

3) x-intercepts

(2.0) , (10,0) x-intercepts

(6, -16) turning point (minimum)

(0,20)

500

for y = - x² + 5, find the:

1) turning point & describe it

2) y intercept

3) x-intercepts

(0,5) turning point (maximum) & y-intercept

(2.236, 0), (-2.236, 0) x-intercepts

finding 'dem zeros

100

find the zeros x² + 7x + 12

-4,-3

200

find the zeros x² + 9x + 14

-7,-2

300

find the zeros x² + 9x + 20

-5,-4

400

find the zeros x² + 11x + 28

-7,-4

500

find the zeros x² + 6x - 27

3,-9

completing the square, MAN

100

complete the square

x² + 16x + ____

64

200

complete the square

x² - 24x + ____

144

300

find the turning point by completing the square:

x² - 4x + 6 = 0

(2,2)

400

find the turning point by completing the square:

x² + 6x - 7 = 0

(-3,-16)

500

find the turning point by completing the square:

x² + 20x + 40 = 0

(-10,-60)

derivatives for relivatives

100

find the derivative of:

y = x² + 3x + 2

^dy/_dx = 2x + 3

200

find the derivative of:

y = 4x³ + 2x² + 2

^dy/_dx = 12x² + 4x

300

find the derivative and slope of tangent line at x = -2 for:

y =  3x² - 5x + 1

^dy/_dx = 6x -5

when x = -2, ^dy/_dx = -3

400

find the derivative and the equation of the tangent 

line @ x = 3 for:

y = x² -4x + 4

^dy/_dx = 2x - 4

y = 2x - 5

500

find the derivative and the equation of the tangent 

line @ x = 1 for:

y = 7x² + 9x + 3

^dy/_dx = 14x + 9

y = 23x - 4

qqqqquadratic formula

100

Use the Quadratic Formula to find the roots of:

x² + 7x + 6 = 0

(6,0) & (1,0)

200

Use the Quadratic Formula to find the roots of:

x² - 2x - 5  = 0

(-1.45,0) & (3.45,0)

300

Use Quadratic Formula to find the roots of:

x² - 8 = 0

(2.828,0) & (-2.28,0)

400

Use the Quadratic Formula to find the roots of:

-x² + 6x + 3

(6.464,0) & (-0.464,0)

500

Use the Quadratic Formula to find the roots of:

3x² - 14x = 0

(0,0) & (4.667,0)