Solve each equation by factoring.
x2+6x+8=0
x=-2, x=-4
4x2 + 25 = 125
x= 5 or x = -5
m2 − 5m − 14 = 0
x=7, x=−2
what is the standard form of a quadratic? Which part gives you the y-intercept?
ax2+bx+c=0
y-intercept is always (0, c)
square root (81)
9
p2 + -2p - 10 = 5
x=5, x=-3
(4x + 1)2 - 16 = 0
x = 3/4 or x = -5/4
b2 − 4b + 4 = 0
x=2
If you have the x-intercepts, how do you find the vertex?
1) half way between them is the axis of symmetry (the x-value of the vertex)
2) plug that into the original equation to get the y-value of the vertex
square root (169)
13
9n2+39n +36 = 0
x=-4/3, x=-3
2x2+10=8
x=i or x=-i
2x2 − 3x − 5 = 0
x=5/2 , x=−1
what is i? what is i7?
i = squareroot of -1
i7= i4*i3 = (1)(-i) = -i
square root (-25)
5i
7r2 + 84 = -49r
x=-4, x=-3
34 = (a - 2)2 - 2
a = 8 or a = -4
9n2 = 4 + 7n
x= (7 + square root of 193) / 18
x= (7 - square root of 193) / 18
What shape do all quadratic graphs have? how do you know if it faces up or down?
quadratic equations graph as parabolas.
the a tells us if it faces up (positive) or if it faces down (negative)
square root (56)
4 square root (14)
3v2 + 7v = 40
x=8/3, x=-5
0 = 3(x + 7)2 - 24
x = -7 + 2 square root of 2
or
x = -7 - 2 square root of 2
4v2=-11-7v
v= (-7 + i squareroot of 127)/8
or
v= (-7 - i squareroot of 127)/8
When is Ms. Heredia having the baby?
Christmas!
square root (-147)
7i square root (3)