6.3 The location of a parabola with respect to the x-axis

• Wiskunde
• Middelbare school

Good morning!

Schedule: 

• 6.3 Learning goals 
• Theory
• Practice together OR practice by yourself 
• Work on the homework 

Learning goals 

At the end of the lesson I can: 

• Calculate the number of x-intercepts of a quadratic equation 
• Sketch the graph of a quadratic equation 
• Explain what a parameter is 
• Calculate with parameters

Theory A: Parabola and discriminant 

What do we calculate in the equation: 

2x²-3x-1 = 0 

We solve for x, but why did we solve for x? 

Theory A: Parabola and discriminant 

What do we calculate in the equation: 

2x²-3x-1 = 0 

We solve for x, but why did we solve for x? 

To find the x-intercept! 

If y=0 we find the x-intercept of the graph!

This is the graph of the formula f(x) = 2x²-3x-1

How many x-intercepts does this graph have? 

What is the discriminant of the equation 2x²-3x-1 = 0?

This is the graph of the formula f(x) = 2x²-3x-1

How many x-intercepts does this graph have? 

The graph has 2 x-intercepts.

What is the discriminant of the equation 2x²-3x-1 = 0?

D = b²-4ac = (-3)²-4·2·-1 = 9 +8 = 17

D > 0 

This is the graph of the formula f(x) = x² - 6x + 9

How many x-intercepts does this formula have? 

What is the discriminant of the equation x² - 6x + 9 = 0?

This is the graph of the formula f(x) = x² - 6x + 9

How many x-intercepts does this formula have? 

The graph has exactly 1 x-intercept. 

The graph is tangential to the x-axis.

What is the discriminant of the equation x² - 6x + 9 = 0?

D = b-4ac = (-6)2-4·1·9 = 36 - 36= 0

D = 0 

This is the graph of the formula f(x) = x² + 4x + 7

How many x-intercepts does this formula have? 

What is the discriminant of the equation x² + 4x + 7 = 0?

This is the graph of the formula f(x) = x² + 4x + 7

How many x-intercepts does this formula have? 

The graph has 0 x-intercepts 

What is the discriminant of the equation x² + 4x + 7 = 0?

D = b2-4ac = 42-4·1·7 = 16 - 28 = -12

D < 0 

To summarize ...

Theory B: Functions with a parameter

Take the function f(x) = 2x2 - 6x + p 

We can fill in any number we like for P: 

f(x) = 2x2 - 6x + 3

f(x) = 2x2 - 6x - 15 

f(x) = 2x2 - 6x + 0

We have an infinite amount of functions!!

Example

Given the function f(x) = 2x2 - 6x + p and point A(-3, 30) on the graph of f. 

Calculate p

Calculate p given the function

and point A(-3,30) on the graph

f(x)=2x​2​​−6x+p

Example

Given the function f(x) = 2x2 - 6x + p and point A(-3, 30) on the graph of f. 

Calculate p

A(-3, 30) gives x=-3 and y= 30. 

30 = 2(-3)2-6·(-3)+p

30 = 2·9 + 18 + p 

30 = 36 + p 

-6 = p                                                 

 f(x) = 2x2 - 6x - 6 with A(-3, 30) on the graph of f

Take out your diaries 

Homework for Thursday 1-4-2021:

Havo                  p. 18-20: #25-32

Raise your hand if you want to practice (with homework questions) together on the board. 

For the people at home as well, raise your hand if you want to practice together. 

If you want to practice by yourself you can start on the homework. 

Raise your hand if you want to practice (with homework questions) together on the board.

For the people at home as well, raise your hand if you want to practice together.

If you want to practice by yourself you can start on the homework. 

Learning goals 

At the end of the lesson I can: 

• Calculate the number of x-intercepts of a quadratic equation 
• Sketch the graph of a quadratic equation 
• Explain what a parameter is 
• Calculate with parameters