Characteristic of Quadratics
The axis of symmetry
What the vertical line that goes through the vertex of a parabola
(5p 2 − 3) + (2p 2 − 3 p 3 )
−3 p 3 + 7p 2 − 3
6v(2v + 3)
12v 2 + 18v
6p 2 − 2 p − 3 = 0
76
𝑥𝑥 2 + 6𝑥𝑥 + 5 = 0
−5 and − 1
The Vertex
What is a point where two lines or rays meet forming an angle at that point
(4 + 2n 3 ) + (5n 3 + 2)
7n 3 + 6
2x(−2x − 3)
−4x 2 − 6x
−4m 2 − 4m + 5 = 0
96
𝑥𝑥 2 – 8𝑥𝑥 + 15 = 0
3 and 5
X intercept
What is the curve value of the x cordinate
(3a 2 + 1) − (4 + 2a 2 )
a 2 − 3
(2n + 2)(6n + 1)
12n 2 + 14n + 2
r 2 + 5r + 2 = 0
17
𝑥 2– 5𝑥 – 24 = 0
−3 and 8
y intercept
What is the curve value of the y coordinate
(5a + 4) − (5a + 3)
1
(x − 3)(6x − 2)
6x 2 − 20x + 6
Find the discriminant of the quadratic equation then state the numberof real and imaginary solutions.
9n 2 − 3n − 8 = −10
−63; two imaginary solutions
𝑥𝑥 2 – 6𝑥𝑥 + 9 = 0
3 only
The minimum
What is the point at which a function's value is greatest
(−4k 4 + 14 + 3k 2 ) + (−3k 4 − 14k 2 − 8)
−7k 4 − 11k 2 + 6
(6p + 8)(5p − 8)
30 p 2 − 8p − 64
Find the discriminant of the quadratic equation then state the numberof real and imaginary solutions.
−4r 2 − 4r = 6
−80; two imaginary solutions
𝑥2 + 8𝑥 – 9 = 0
1 and − 9