# 6.1 parabolas and equations

Good morning!
Schedule:
• 6.1 Learning goals
• Theory
• Homework questions?
• Work on the homework
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Slide 1: Slide
WiskundeMiddelbare schoolhavoLeerjaar 3

This lesson contains 17 slides, with interactive quizzes and text slides.

## Items in this lesson

Good morning!
Schedule:
• 6.1 Learning goals
• Theory
• Homework questions?
• Work on the homework

#### Slide 1 -Slide

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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
- Calculate the x-intercept of a graph
- Calculate the y-intercept of a graph

#### Slide 2 -Slide

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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)=43x2+3x2
Given is the function
Point A is on the graph and has the x-coordinate xA= -2

f(2)=43(2)2+3(2)2
f(2)=434+122
f(2)=41214=314=11

#### Slide 3 -Slide

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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+43+1
g(3)=39+43+1
g(3)=27+12+1
g(3)=14
Yes! Point B is on the graph of g(x)

#### Slide 4 -Slide

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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)

#### Slide 5 -Slide

this is exercise 9 of the homework
Where on the y-axis are the x-intercepts? (the green points)

#### Slide 6 -Open question

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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)=x2+2x15
0=x2+2x15

#### Slide 7 -Slide

this is exercise 9 of the homework

Solve for x
x2+2x15=0

#### Slide 8 -Open question

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Theory B: x- and y- intercepts of graphs
Product-sum-method:

x = 3  v  x = -5

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

(x3)(x+5)=0
x+2x15=0
product
sum
1 · -15
-15
3 · -5
-2
-3 · 5
2
(x3)(x+5)=0

#### Slide 9 -Slide

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)

#### Slide 10 -Slide

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?

#### Slide 11 -Slide

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)=x2+2x15
f(0)=02+2015
f(0)=15

#### Slide 12 -Slide

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!

#### Slide 13 -Slide

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Homework for Monday 15-3-2021:
Havo                  p. 10-13: #1-11 (9)

#### Slide 14 -Slide

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Homework questions?

#### Slide 15 -Slide

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I want to try this myself in the homework
I want to solve some equations together

#### Slide 16 -Poll

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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