# 1718 WH3X CH2 Lesson 5

Finding the vertex
(without spending a lot of time plotting the graph...)
1 / 11
Slide 1: Tekstslide
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In deze les zitten 11 slides, met tekstslides.

Lesduur is: 50 min

## Onderdelen in deze les

Finding the vertex
(without spending a lot of time plotting the graph...)

#### Slide 1 -Tekstslide

Vertex
The vertex is the highest (downward opening parbola)
or lowest (upward opening parabola) point of a parabola.

The vertex lies on the axis of symmetry
Therefore, the x-coordinate of the vertex is the same as the x-value of the axis of symmetry.

#### Slide 2 -Tekstslide

Axis of symmetry
Since the axis of symmetry divides the parabola into two equally shaped halves, the x-value of the axis of symmetry can be found halfway between two points on the parabola with the same y-value.

#### Slide 3 -Tekstslide

(-3,0) and (-1,0) have the same
y-value. The vertex is then in the
middle of x = -3 and x = -1, so at x = -2.
(Notice that that is also
between x = -4 and x = 0)
Fill in -2:
The vertex is then at (-2, -1)

y=x2+4x+3
y=(2)2+42+3=1

#### Slide 4 -Tekstslide

(1,0) and (3,0) have the same
y-value. The vertex is then in the
middle of x = 1 and x = 3, so at x = 2.
(Notice that that is also
between x = 0 and x = 4)
Fill in 2:
The vertex is then at (2, -0.5)

y=0.5x22x+1.5
y=0.52222+1.5=0.5

#### Slide 5 -Tekstslide

(0,-3) and (3,-3) have the same
y-value. The vertex is then in the
middle of x = 0 and x = 3, so at x = 1.5
(Notice that there are no points of
intersection with the horizontal axis)
Fill in 1.5:
The vertex is then at (1.5, -0.75)

y=x2+3x3
y=11.52+31.53=0.75

#### Slide 6 -Tekstslide

(-5,-2) and (0,-2) have the same
y-value. The vertex is then in the
middle of x = -5 and x = 0, so at x = -2.5
(Notice that the points of intersection
with the x-axis are not easy to use)
Fill in -2.5:
The vertex is then at (-2.5, 4.25)

y=x25x2
y=1(2.5)252.52=4.25

#### Slide 7 -Tekstslide

Calculating the vertex
1) Find two points on the parabola with the same y-value (points of intersection with the x-axis or with the horizontal line through the point of intersection with the y-axis).
2) Find the x-value of the axis of symmetry in the middle of those two points.
3) Fill in the x-value in the formula to calculate the y-value
4) Write down the coordinates of the vertex

#### Slide 8 -Tekstslide

Example
Calculate the coordinates of the vertex of the parabola with formula:
1) If x = 0, y = -8, so point of intersection y-axis = (0, -8)

or

y=3x2+12x8
3x2+12x8=8
3x2+12x=0
3x(x+4)=0
3x=0
x=0
x+4=0
x=4

#### Slide 9 -Tekstslide

Example
1)                          or
2) So axis of symmetry is at
3) Fill in:
4) Coordinates vertex are: (-2, -20)

x=0
x=4
x=2
y=3(2)2+1228=20
y=3x2+12x8

#### Slide 10 -Tekstslide

Homework Tuesday
§2.2:
Make ALL key exercises: 10, 13, 14, 15
Make AT LEAST 1 from the basic: 11, 12 or advanced exercises: 16