Quadratics Flashcards
What is a quadratic?
Any expression in which the highest power is 2
What is standard form for a quadratic expression?
ax^2 + bx + c = 0
(x + 4) (x - 2) = 0
FOIL
x^2 - 2x + 4x - 8
= x^2 + 2x - 8
x^2 + 7x + 12 = 0
What multiplies to equal 12 and adds to equal 7
(x + 3) (x + 4) = 0
What are the solutions of (x + 3) (x + 4) = 0 ?
Set each one equal to zero so
x + 3 = 0 so x = -3
x + 4 = 0 so x = -4
and then you write those solutions as {-3, -4}
What is (x + y)^2 ?
x^2 + 2xy + y^2
(x - y)^2
x^2 - 2xy + y^2
(x + y) (x - y) = ?
x^2 - y^2
This is a difference of two squares
What is 16 - y^2 = ?
(4 + y) (4 - y)
factor x^2 + x = 20
x^2 + x - 20 = 0
(x + 5) (x - 4)
so, the solutions are {-5, 4}
x^2 + kx + 12 = 0
k is a constant
a^2 + b^2 = 16
(a + b)^2 = 30
For the equations above, what is the value of ab?
ab = 7
a^2 + 2ab + b^2 = 30
since it is given that a^2 + b^2 = 16 you can substitute that in so first rearrange
a^2 + b^2 + 2ab = 30
then substitute
16 + 2ab = 30
ab = 7
x^2 + 15x + 56 = 0
What is the difference between the greatest and least roots of the equation above?
(x + 8) (x + 7)
-7 - - 8 = -7 + 8 = 1
answer = 1
Also note for difference you subtract from the largest value of the two
what are roots?
solution of a quadratic
what are zeros?
solutions of a quadratic
