Parabolas

Question 1

What is a parabola?

Answer 1

Parabola = graph of a quadratic expression

Question 2

What are the two possible shapes for a parabola?

Answer 2

• smooth, symmetrical ‘smiley face’ or ‘sad face’

Question 3

What are the 5 important features of a parabola?

Answer 3

-> SHAPE - a “happy” or “sad” face (“sad” when coefficient of x^2 is negative, “happy” when coefficient of x^2 is positive”
-> Y-INTERCEPT - y value when x=0
-> ROOTS - solutions for x when y=0
-> VERTEX - coordinate of top/bottom (tip of curve)
-> LINE of SYMMETRY - line through vertex

Question 4

How do u plot parabolas?

Answer 4

• w/ a table of coordinates, substitute urself or use calculator
• check graph is a smooth shape!
• for parabolas, no need to draw out of coordinates calculated (unless it’s a sketch)

Question 5

What is the form of a linear expression?

Answer 5

y = mx + c

Question 6

What is the form of a quadratic expression?

Answer 6

y = ax^2 + bx + c

Question 7

How many roots can a parabola have?

Answer 7

a PARABOLA can have 0, 1, 2 roots depending on where it is in relation to the axes

Question 8

What is another word for the ‘vertex’ of a parabola?

Answer 8

The ‘vertex’ is also called a TURNING POINT + can either be a minimum or a maximum depending on the shape of a parabola

Question 9

Review how to do function notation!!! (on GC, notability, DrFrost)

Answer 9

Good luck!!!

Question 10

How do u sketch a parabola?

Answer 10

1. Simple axes (no scale or ticks)
2. Find the key features (shape, y-intercept, roots, vertex)
3. Mark values in approx. positions on axes
4. Smooth curve to connect it all together

Question 11

Do practice questions on all aspects of parabolas (on GC/notability/DrFrost)

Answer 11

Good luck!!!