Forms/Equations of a Quadratic
What is the shape of a quadratic function's graph?
Parabola
Describe the transformation of the parent function, given the following equation:
y=(x-4)^2+1
Shift right four units; up one unit
Solve the following function with a graphing calculator:
2x^2+12x=0
x = 0, -6
Solve the quadratic using square roots:
x^2-49=0
x=-7,7
x=(-b+-sqrt(b^2-4ac))/2a
What is the standard form of a quadratic function?
y=ax^2+bx+c
Describe the transformation of the parent function, given the following equation:
y=x^2-6
6 units down
Solve the following function with a graphing calculator:
2x^2+3x-5=0
x=1, -2.5
Solve the following quadratic by taking the square root:
3x^2-108=0
x= -6,6
Solve the quadratic using the Quadratic Formula:
x^2-2x-48=0
x= -6, 8
What is the following form of a quadratic called?
y=a(x-h)^2+k
Vertex Form; (h,k) is the vertex of the quadratic function.
Describe the transformation of the parent function, given the following equation:
y=(x+7)^2
Shift 7 units to the left
Solve the following function by factoring:
x^2-6x=0
x = 0, 6
Complete the Square to rewrite the following equations in the form
(x^2+m)=c
:
x^2+4x-5=0
(x+2)^2=9
Solve the quadratic using the Quadratic Formula:
6x^2-15=0
x=5/2, 0
Given a quadratic in standard form, how can you find the equation for the axis of symmetry?
y=-b/(2a)
Describe the transformation of the parent function, given the following equation:
f(x)=2(x-40)^2-2
Vertical Stretch of 2, Shift 40 units to the right, 2 units down
Solve the following function by factoring:
x^2+3x+2=0
x=-1, -2
Complete the Square to rewrite the following equations in the form
(x^2+m)=c
:
x^2+2x-50=-2
(x+1)^2=49
Describe the transformation of the parent function, given the following equation:
f(x)= -3(x+2)^2-1
Reflection over x-axis, Vertical Stretch of 3; 2 units to the left, one unit down.
Solve the following function by factoring:
x^2-4x-21=0
x=7, -3