## How do we identify them?

· The second difference is the same

· The graph is in the shape of a parabola/ a U.

· The eq’n has an ** x2** value.

## Everything you need to know about parabolas.

· Parabolas can open up or down.

· The zero of a parabola is where the graph crosses the **x–axis**.

· Zero can also be called **roots** or **x-intercept.**

· The **axis of symmetry **divides the parabola into 2 equal halves.

· The **y-intercept **of a parabola is where the graph crosses the **y-axis**.

· The **optimal value** is where the graph is at its maximum or minimum.

· The **vertex** is the point where the **axis of symmetry **and** optimal value **cross.

## How parabolas move.

__Vertical movement __

· y = x2 + 3 à Translates up 3 units

· y = x2 – 3 à Translates down 3 units__Vertex movment__

· +k à when k is positive the movment is up

· –k à when k is negative the movment is down__Horizontal movment __

· y = (x + 3)2 à translates 3 units left

· y = (x – 3)2 à translates 3 units right__Compression/Stretch__

· y = __1__x2 à vertically compressed by a factor of __1__

2 2

· y = 2x2 à vertically stretched by a factor if 2__Reflection __

· y =– x2 à reflected in the x – axis

· when a is positive, it opens upwords.

· When a is negative, it opens downwards. **y = a(x – h)2 + k**__k__

(+) up

(-) down__h__

(+) right

(-) left__a__

(+) opens up

(-) opens down

(whole #) stretched

(faction) compressed

## Moving Quadratics

**When a basketball is trown upward, it’s path can be modelled by the function:**

y = –4.5(x – 0.1u)2 + 4

When u is velocity(speed)

x is time

y is the height**a. What is the eq’n when the ball is thrown with a velocity of 12m/s? **

· sub 12 into u

y = –4.9 (x – 0.1(12))2 + 9

y = –4.9 (x – 1.2)2 + 9**b. How many seconds after it is thrown does the ball reach the highest point?**

Since the vertex is (1.2,9) we know that it reaches the maximum height of 1.2s.