Refresh: lesson 1, 2

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

Quadratic expressions

Lesson 1

Find the axis of symmetry using

y=x​2​​−6x+10

x=−​2a​​b​​

and find the vertex that belongs with this function

y=x​2​​−6x+10

Find the axis of symmetry using

y=−x​2​​−8x+12

x=−​2a​​b​​

and find the vertex that belongs with this function

y=−x​2​​−8x+12

Finding the axis of symmetry

Left you can see the graph of 

You can find the x-coordinates where the parabola intersects the x-axis bij solving

-> x(x+4)=0

-> x=0 or x+4 = 0

x= 0 or  x = -4

The axis of symmetry is lying in the middle of these points , so at x=-2

f(x)=x​2​​+4x

x​2​​+4x=0

Find the axis of symmetry

y=(x+5)(x−3)

and find the vertex

y=(x+5)(x−3)

Find the axis of symmetry

y=2x(x−3)

and find the vertex

y=2x(x−3)

Complete the square

y=x​2​​+12x−25

Complete the square and find the axis of symmetry

y=x​2​​−2x+14

Lesson 2

3. I can explain from f(x) = a(x-s)(x-t) the characteristics of a, s and t

  

4. I can read of the points of intersection with the x-axis and use these to find the axis of symmetry and the coordinates of the vertex

Give the points of intersection with the x-axis from the function

f(x)=(x+2)(x−3)

Up or downward?

f(x)=(x+2)(x−3)

Give the points of intersection with the x-axis from the function

g(x)=2(x+2)(x−3)

Up or downward?

g(x)=2(x+2)(x−3)

Give the points of intersection with the x-axis from the function

h(x)=−2(x−2)(x+3)

Up or downward?

h(x)=−2(x−2)(x+3)

witch function is the narrowest f(x) or g(x)?

f(x)=(x+2)(x−3)

g(x)=2(x+2)(x−3)

witch function is the narrowest f(x) or g(x)?

f(x)=(x+2)(x−3)

g(x)=​2​​1​​(x+2)(x−3)

witch function is the narrowest f(x) or g(x)?

f(x)=−2(x+2)(x−3)

g(x)=2(x+2)(x−3)

The graph of the function f(x)=2(x-s)(x-t) passes through the points (-6,0) and (3,0)

1. Write down the correct formula.

The function from the slide earlier is f(x)=2(x+6)(x-3)

2. Write down the equation for the axis of symmetry

From the graph of the function f(x)=2(x+6)(x-3) the equation for the axis of symmetry is y= -4.5

3. Calculate the coordinates of the vertex