6.2 Intro to Quadratics

6.2 Intro to Quadratics

We're going to go through this lesson together.

The graph gives the height of a water bottle rocket with respect to time.

Think: What do the x-axis and y-axis mean in context?

Multiple Choice

What happens to the rocket at 4 seconds?

• The rocket lands

• The rocket starts to fall back to earth

• The rocket is still going up

• The rocket lifts off

A U-shaped graph is called a parabola

A parabola is a quadratic function.

Multiple Choice

A parabola is a quadratic function. It's largest exponent is ______

• 1

• 2

• 3

• 4

• 5

The special point on a graph where the parabola starts is called the vertex.

Multiple Choice

Identify the vertex

Remember, in an ordered pair looks like (x,y)

• (3,0)

• (3,1)

• (0,3)

• (3,-3)

The highest/lowest point on a graph is called the maximum/minimum

This is a y-value.

Multiple Choice

If a parabola opens upward, the vertex is the lowest point.

What is this called?

• Maximum @ y = 0

• Minimum @ y = 0

The line that divided the parabola in half is called the axis of symmetry

Always starts with x=

In this example: x=4

The parabola crosses the x-axis at zeros

Zeros are also called roots or x-intercepts.

These zeros are x = 0 and x = 8

If we wrote them as x-intercepts, we would say (0,0) and (8,0).

Multiple Select

Identify the zero(s) (select all that apply)

• x = 3

• x = 2

• x = 0

• x = 4

• none

Domain is the set of all x-values

Multiple Choice

Identify the domain

• all real numbers

• x > 0

• y >= 0

• (2,1)

Range is the set of all y-values

Multiple Choice

Identify the range

• all real numbers

• x > 0

• y >= 0

• (2,1)

More Practice

We will do these together, but you might have to try on your own a little bit :)

Multiple Choice

Identify the vertex

• (1,4.5)

• (4.5,1)

• (-2,0)

• (4,3)

Multiple Choice

If a parabola opens downward, the vertex is the highest point.

What is this called?

• Maximum @ y = 4.5

• Minimum @ y = 4.5

Multiple Select

Identify the x-intercept(s) (select all that apply)

• (-2,0)

• (4,0)

• (4.5,1)

• (0,-2)

• none

Multiple Choice

Identify the domain

• all real numbers

• x > 4.5

• y <= 4.5

• (1,4.5)

Multiple Choice

Identify the range

• all real numbers

• x > 4.5

• y <= 4.5

• (1,4.5)

Great! Let's try some more!

Ask a question if you're struggling :)

Multiple Choice

Identify the vertex

• (0,1)

• (1,0)

• 1

• (2,2)

• none

Multiple Choice

Does this parabola have a maximum or minimum?

• Maximum @ y = 1

• Minimum @ y = 1

Multiple Select

Identify the x-intercept(s) (select all that apply)

• (1,0)

• (0,1)

• none

• (0,-2)

• (1,1)

Multiple Choice

Identify the domain

• all real numbers

• x > 1

• y >=1

• (0,1)

Multiple Choice

Identify the range

• all real numbers

• x > 1

• y >=1

• (0,1)