Updated Chapter 3

This is a second-degree function

What is a Quadratic Function?

What is the equation for a quadratic function?

f(x)= ax²+bx+c

These are called turning points on a parabola

What is the vertex?

This means that the graph is symmetric about a vertical line through the vertex

What is the axis of symmetry?

If a parabola concaves upwards, what does that mean?

This means that a is positive, and the vertex is a minimum

If a parabola concaves downward, what does that mean?

This means that a is negative, and the vertex is a maximum.

What does the red mean?

The graph is increasing from x=0 to x=2

What does the green mean?

The graph is decreasing from x=2 to x=4

The formula for a vertex?

x=-b/2a

Find the vertex of this function : f(x)=2x²+4x+3

Do the vertex formula: -4/2(2)= -1

What is the vertex form?

y=a(x-h)²+k

Vertex: (h,k)

! You flip the value of h, but keep k the same !

Find the vertex of the parabola: y= -3(x-5)²+2

The vertex of the parabola is at the point (5, 2).

The vertex of a parabola is (1,7) and one point on the parabola is (2,-2). Find the equation of the parabola

! y=a(x-h)²+k !

• -2=a(2-1)²+7

• -2=a+7

• y=-9(x-1)²+7

Solve by factoring: -16t²+64t+80=0

1) Divide by sides by -16

• t²-4t-5=0

2) You need to find two values that multiply the c value and add to the b value

• (t-5)(t+1)=0

3) Flip the signs: t=5, -1

Solve 1400=-0.01x²+20x-500 using the intersection method.

1) y1= 1400

2) y2= -0.01x²+20x-500

! find where they intersect

The square root method: 2(x-3)²=10

1) Divide both sides by 2

• (x-3)²=5

2) Square root both sides

• x-3= +- square root 5

Completing the square

• Take half of the middle coefficient , then square it .

x²-4x-1=0: Complete the square

• Half of -4 =-2

• Square of -2 = 4

New Equation) x²-4x+4=1+4

(x-2)²= +- square root 5 : x-2=+-√5

What is this formula?

This is the Quadratic Formula

Quadratic formula: if b²-4ac is greater than 0 . . .

There will be two different real solutions

Quadratic formula: if b²-4ac=0 . . .

There is one real solution

Quadratic formula: if b²-4ac is less than zero . . .

There is no real solution

How do you graph these?

Look at if #<x<#, graph the equation