6.1 parabolas and equations

• Wiskunde
• Middelbare school
• havo
• Leerjaar 3

Good morning!

Schedule:

• 6.1 Learning goals 
• Theory 
• Homework questions?
• Work on the homework 

6.1 Parabolas and equations 

At the end of this lesson I can: 

- Calculate the y-coordinates of points on a parabola 

- Calculate if a point is on a graph 

- Solve a quadratic equation 

- Calculate the x-intercept of a graph 

- Calculate the y-intercept of a graph 

Theory A: Points on parabolas

To find the y-coordinate of a point on a graph, we fill in the x-coordinate in the formula of the graph: 

f(x)=​4​​3​​x​2​​+3x−2

Given is the function

Point A is on the graph and has the x-coordinate x_A= -2

f(−2)=​4​​3​​(−2)​2​​+3⋅(−2)−2

f(−2)=​4​​3​​⋅4+−12−2

f(−2)=​4​​12​​−14=3−14=−11

Theory A: Points on parabolas

If we want to check if a point is on a graph, we fill in the x-coordinate and see if the y-coordinate matches

Is point B (3,-14) on the graph of g(x) = -3x²+4x + 1?

g(3)=−3⋅(3)​2​​+4⋅3+1

g(3)=−3⋅9+4⋅3+1

g(3)=−27+12+1

g(3)=−14

Yes! Point B is on the graph of g(x)

Theory B: x- and y- intercepts of graphs

We can find the x-intercepts where the graph intersects the x-axis.

Where on the y-axis are the x-intercepts? (the green points)

this is exercise 9 of the homework 

Where on the y-axis are the x-intercepts? (the green points)

Theory B: x- and y- intercepts of graphs

We find the x-intercepts where y=0 

we fill this in, in the formula: 

Solve for x!

f(x)=x​2​​+2x−15

0=x​2​​+2x−15

this is exercise 9 of the homework 

Solve for x

x​2​​+2x−15=0

Theory B: x- and y- intercepts of graphs

Product-sum-method:

x = 3  v  x = -5 

A(3,0) and B(-5,0)

(x−3)(x+5)=0

x+2x−15=0

product	sum
1 · -15	-15
3 · -5	-2
-3 · 5	2

(x−3)(x+5)=0

this is exercise 9 of the homework 

Theory B: x- and y- intercepts of graphs

To find the y-intercept

      Same idea

Where on the x-axis is the y-intercept? (the blue point)

this is exercise 9 of the homework 

Theory B: x- and y- intercepts of graphs

x = 0! We fill this in, in the formula. 

What are the coordinates of point C, the y-intercept of this graph? 

this is exercise 9 of the homework 

Theory B: x- and y- intercepts of graphs

x = 0! We fill this in, in the formula. 

Point C (0,-15)

f(x)=x​2​​+2x−15

f(0)=0​2​​+2⋅0−15

f(0)=−15

this is exercise 9 of the homework 

To summarize

If you need to find the y-intercept              x=0

If you need to find the x-intercept              y=0

To find the other coordinate, you fill 0 in the formula in the right place!

Take out your diaries 

Homework for Monday 15-3-2021:

Havo                  p. 10-13: #1-11 (9)

Homework questions?

Open your notebook and see if you had any questions about your homework. 

Solve quadratic equations

I want to try this myself in the homework

I want to solve some equations together

6.1 Parabolas and equations 

At the end of this lesson I can: 

- Calculate the y-coordinates of points on a parabola 

- Calculate if a point is on a graph 

- Solve a quadratic equation 

- Calculate the x-intercept of a graph 

- Calculate the y-intercept of a graph