Solve each equation by factoring.
p2 + -2p - 15 = 0
5, -3
4x2 + 25 = 125
x= 5 or x = -5
m2 − 5m − 14 = 0
{7, −2}
The name given to the shape of a quadratic function
Parabola
The following key words tell us we are looking for which peices of the quadratic?
a) "when- highest point"
b) "height- highest point"
c) "ground"
a) x in vertex
b) y in vertex
c) solution (x-intercept)
9n2 + 39n +36= 0
-4/3, -3
(4x + 1)2 - 16 = 0
x = 3/4 or x = -5/4
b2 − 4b + 4 = 0
{2}
The name given to the maximum/minimum point of a quadratic function
Vertex
A pitcher throws a ball in the air. The ball is modelled by the equation given below, where x is the time, in seconds, and y is the height, in feet. When is the ball at its peak?
y=-16x^2+96x+6
3 seconds.
r2 +7r+ 12 = 0
-4, -3
34 = (a - 2)2 - 2
a = 8 or a = -4
2x2 − 3x − 5 = 0
{5/2 , −1}
The name given to the line that splits a quadratic function into a mirror image of itself
Axis of symmetry
A pitcher throws a ball in the air. The ball is modelled by the equation given below, where x is the time, in seconds, and y is the height, in feet. What is the highest point that the ball reaches?
y=-16x^2+96x+6
150 ft
3v2 + 7v -40= 0
8/3, -5
0 = 3(x + 7)2 - 27
x = -10, -4
6n2 +4n-59 =7
x = 3, -11/3
How you know an equation is a quadratic
A pitcher throws a ball in the air. The ball is modelled by the equation given below, where x is the time, in seconds, and y is the height, in feet. How long is the ball in the air? (Round to the nearest tenth of a second)
y=-16x^2+96x+6
6.1 seconds