Vertex to standard
Standard to vertex
Standard to vertex
Tell whether the quadratic function is in vertex form or standard form.
1. y=x2-2x-35
2. y=-4(x-2)2+4
1. standard form
2. vertex form
Determine the product.
(4i − 5)(4i + 5)
= 16 i2 + 20i − 20i − 25
= 16(−1) − 25
= −41
Determine the roots of each quadratic equation.
1. x2+5x+6=0
2. x2-3x-4=0
1. The roots are -3 and -2
2. The roots are 4 and -1
For each inequality, will there be a solid or dashed line on the graph?
1. x ≥ 0
2. −x + y > 0
3. 2x + y > 6
4. 2x + y ≤ 10
1. solid
2. dashed
3. dashed
4. solid
How many solutions does this system have?
What are the solutions?
y = x2 − 6x + 7
y = 2x
The system has two solutions.
The solutions are (7,14) and (1,2)
Change the vertex form equation into standard form using the foil or box method.
y=2(x-3)2+4
y=2x2-12x+22
Simplify the expression.
(2 + 5i) − (7 − 9i)
= 2 + 5i − 7 + 9i
= (2 − 7) + (5i + 9i)
= −5 + 14i
Determine the zeros of each quadratic equation.
1. x2 − 12x + 25 = 0
2. x2 + 10x + 2 = 0
1. The zeros are approximately 9.32 and 2.68.
Check: (9.32)2 − 12(9.32) + 25 ≈ 0 (2.68)2 − 12(2.68) + 25 ≈ 0
1. The roots are approximately − 0.20 and − 9.80.
Check: (−0.20)2 + 10(−0.20) + 2 ≈ 0 (−9.80)2 + 10(−9.80) + 2 ≈ 0
What is the definition of absolute value?
Absolute value is the distance between the number and zero.
What are the solutions to the system of equations?
5x + y − 2z = 5
3x + 4y − z = − 7
x − 5y + 2z = 19
The solution to the system is x = 2, y = − 3, and z = 1.
Change the standard form equation into vertex form using DESMOS. List the vertex, y-intercept, and x-intercepts.
y=3x2-6x+8
Vertex: (1,5)
y-intercept: (0,8)
x-intercepts: none
Simplify the expression.
−(4i − 1 + 3i) + (6i − 10 + 17)
= (−4i − 3i + 6i) + (1 − 10 + 17)
= −i + 8
Determine the x-intercepts of each equation.
1. -t2+12t=32
2. w2+5w-32=2w-4
1. The x-intercepts are 4 and 8
2. The x-intercepts are -7 and 4
Given the absolute value below, what is the vertex, domain, range, maximum, and minimum?
y=− |x + 1| + 2
vertex:(-1,2)
domain: all real numbers
range: y ≤ 2
maximum: y=2
minimum: none
1. Solve the system of equations.
y = − 2x2 + 8x + 1
y = − 4x + 19
2. What is the term used to describe the line in relation to the parabola on the graph?
1. x=3 y=7
The solution to the system is (3,7)
2. Tangent- A line that touches the parabola exactly at one point.
Change the following equation into standard form using the foil or box method.
y=(x+5)(x+3)
=x2+3x+5x+15
=x2+8x+15
Simplify the expression.
(4 − 5i)(8 + i)
= 32 + 4i − 40i − 5 i2
= 32 + 4i − 40i − 5(− 1)
= (32 + 5) + (4i − 40i)
= 37 − 36i
Solve the quadratic equation.
x(x+2)=143
x=-13
x=11
Given the absolute value below, list the transformations in relation to the parent function y=|x|.
y=−|x + 2| − 1
There will be 3 transformations:
reflection
horizontal shift left 2 units
vertical shift down 1 unit
Solve the system of linear equations.
x=4y-9
2x-8y=10
There is no solution to the system.
Change the vertex form equation into standard form using the foil or box method.
y=-5(x-1)2+4
Also, list the following:
Vertex
h
k
y-intercept
roots
HINT: DETERMINE YOUR ROOTS IN DESMOS
y=-5x2+10x-1
vertex: (1,4)
h=1
k=4
y-intercept: (0,-1)
roots: (0.106,0) and (1.894,0)
List the definitions of each imaginary term.
i1
i2
i3
i4
i1=i
i2=-1
i3=-i
i4=1
Determine the zeros of each equation.
1. 9x2+5x+1
2. f(x)=-x2+6x+7
1. The function has no real zeros
2. x=-1 or x=7
Write a system of inequalities to represent the constraints in each problem situation.
HINT: THERE SHOULD BE 3 INEQUALITY EQUATIONS IN YOUR SYSTEM!
A local runner’s club rented an auditorium seating 600 people to hear a presentation by a world-record runner. Tickets to the event cost $5 for anyone who is 18 years old or younger and $7 for everyone else. The club already knows that at least fifty $5 tickets and two hundred $7 tickets have been sold.
Let x represent the number of $5 tickets sold.
Let y represent the number of $7 tickets sold.
x ≥ 50
y ≥ 200
x + y ≤ 600
Solve the system of equations using substitution. NO DESMOS
y=x2+2x+5
y=5x+15
x2 + 2x + 5 = 5x + 15
x2 − 3x − 10 = 0
(x − 5)(x + 2) = 0
x − 5 = 0 or x + 2 = 0
x = 5 or x = − 2
Substitute x = 5 into the linear equation.
y = 5(5) + 15
y = 40
Substitute x = − 2 into the linear equation.
y = 5(−2) + 15
y = 5
The solutions to the system are (5, 40) and (− 2, 5).