Pre-Calc Corrections Unit 4

Vertical Equation for Parabola

y - k = a (x - h)²

If a>0 for vertical parabola, then parabola opens…

up

If a<0 for vertical parabola, then parabola opens…

down

If a<0 for horizontal parabola, then parabola opens…

left

If a>0 for horizontal parabola, then parabola opens…

right

Equation for a (parabola)

a = 1/(4p)

What are required components of parabola? (6)

1) vertex

2) orientation

3) focal width

4) focus

5) directrix

6) axis of symmetry

How to find orientation for parabola?

a value (a>0 or a<0)

How to find vertex for parabola?

(h,k)

How to find focus for parabola? (3)

1) a = 1/(4p) —> solve for p

2) add & subtract p value from y-value of vertex (vertical orientation) or x-value of vertex (horizontal orientation)

3) You should only get one answer

How to find directrix for parabola? (3)

1) take y-value of vertex (vertical orientation) or x-value of vertex (horizontal orientation)

2) minus p value

3) write in y = (answer)

How to find axis of symmetry for parabola? (2)

1) take y-value of vertex (horizontal orientation) or x-value of vertex (vertical orientation)

2) write it as x = (that value)

How to find focal width for parabola?

absolute value of 4p

Vertical/Horizontal Equation for Ellipse

(x-h)²/a² + (y-k)²/b² = 1

Difference between horizontal and vertical ellipse is….

larger denominator

What are the components of ellipse? (5)

1) Horizontal/Vertical

2) Foci

3) Center

4) Major Axis (vertices)

5) Minor Axis (vertices)

How to find center for ellipse?

(h,k)

How to find major axis vertices for ellipse? (3)

1) If horizontal, take a value (make sure it is a not a²) and add & subtract it to x-value of center

2) Should get two answers

3) Same goes for vertical

How to find minor axis vertices for ellipse? (3)

1) If horizontal, take b value (make sure it is b not b²) and add & subtract it to y-value of center

2) Should get two answers

3) Same goes for vertical

How to find foci for ellipse? (3)

1) a² + b² = c² —> solve for c

2) If horizontal, add and subtract c value to x-value

3) Same goes for vertical

Vertical equation for hyperbolas

-(x-h)²/a² + (y-k)²/b² = 1

Horizontal equation for hyperbolas

(x-h)²/a² - (y-k)²/b² = 1

What are components of hyperbolas? (5)

1) Foci

2) Transverse axis

3) Conjugate axis

4) Center

5) Horizontal/Vertical

How to find foci for hyperbola? (3)

1) a² + b² = c²

2) If vertical, add & subtract c value to y-value of center

3) Same goes for horizontal

How to find center for hyperbola?

(h,k)

Difference between horizontal and vertical hyperbola is….

larger denominator

How to find transverse axis for hyperbola? (3)

1) If vertical, 2b = (answer)

2) Should only get one answer

3) Same goes for horizontal

How to find conjugate axis for hyperbola? (3)

1) If vertical, 2a = (answer)

2) Should only get one answer

3) Same goes for horizontal

Equation/format for Completing the Square

x² + bx + (b/2)² = (x + b/2)²