Graphing
What is vertex form?
y=(x+p)(x+q)
What are the 5 strategies for solving a quadratic equation to identify solutions?
Factor by Grouping
Complete the Square
Quadratic Formula
Square Root Method
Graphing
Simplify
sqrt(72)
+-6sqrt(2)
n^2+14n+48=0
(n+8)(n+6)=0
What is standard form of a quadratic and what letters represent the coefficients?
ax^2+bx+c=0
coefficients: a,b,c
Which way does -x^2 +5 =0 open?
Down
What strategy should be used for x^2-60=4 ?
Square root method
simplify
sqrt(192)
+-8sqrt(3)
(x-3)^2=17
x=
3+sqrt(17)
List the squares of numbers 2-12
4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
What are the x-intercepts in -(x+4)(x-2)=0?
x=-4,2
What strategy should you use for 2n^2+3n-9 ?
Factor by Grouping
What does the polynomial 6x^2-30x+42=0 look like when you factor out the GCF.
6(x^2-5x+7)=0
2x^2+11x+5
(2x+1)(x+5)
What is the procedure/formula to find where the vertex of a parabola is IN INTERCEPT FORM?
(p+q)/2 = x
plug x back into the parabola/function to solve for y. (x,y) is your vertex.
Describe the transformations in
y = -(x+3)^2 -2=0
Shifted left 3 units, shifted down 2 units, opens down.
What strategy should you use for 6x^2-2x-1=0 ?
Quadratic Formula
Simplify
(10+-sqrt(9-(-4)(4)))/5
x=1,3
-4x^2+3x+5
x=(-3+-sqrt(89))/(-8)
What is the quadratic formula?
(-b+-sqrt(b^2-4ac))/2a
Graph y=-(x-4)^2-5=0 . Circle the solutions.
No solutions. Opens down, translated down 5 units and right 4 units.
Under what conditions can you use quadratic equations?
All!
Simplify
(6+-sqrt(81-57))/2
3+-sqrt(6)
x^2+6x+15
No Real Solution
What does the term "solution of a quadratic" mean?
The value of x when the polynomial is set to 0 (y=0). Where the parabola intercepts the x-axis.