Quadratic Functions
If a parabola opens up, will it have an max or a min?
min
How would you convert a quadratic equation in standard form to vertex form?
Complete the square
What is the solution to a system of equations?
A point of intersection
True or False: There is only one solution to an inequality
False
True or False: Mrs. Livermore was born in the 90's
False, I was born in the 80's
If parameter a = 2, parameter p = 4, and parameter q = -1, describe the following characteristics of the parabola:
1) direction of opening
2) shape
3) coordinate of the vertex
4) equation of the axis of symmetry
1) up
2) narrower than the base graph
3) (4, -1)
4) x = 4
How would you convert a quadratic equation in standard form to factored form?
Factor
How many solutions can a linear-quadratic system of equations have?
0, 1, or 2
True or False: The solution to an inequality in one variable is an area or a region on a Cartesian plane?
False, it is an interval on a number line
True or False: Mrs. Livermore likes to sew her own clothes
True!
What characteristic(s) of a parabola do you know when given an equation in vertex form?
1) direction of opening
2) shape
3) vertex
4) axis of symmetry
What characteristic(s) of a parabola do you know when given an equation in factored form?
1) direction of opening
2) shape
3) x-intercepts
How many solutions can a quadratic-quadratic system of equations have?
0, 1, 2, or infinite
If the test point you choose makes the inequality false, should you shade the area containing the test point?
No
2: Margot (age 4), Pierce (age 1.5)
What characteristic(s) of a parabola do you know when given an equation in standard form?
1) direction of opening
2) shape
3) y-intercept
Factor.
y = x2 +11x +24
y = (x +3)(x + 8)
Solve by Substitution.
y=2x
y=x2 + 1
2x = x2 + 1
x2 + 2x + 1 = 0
(x + 1)(x + 1) = 0
x = 1
y = 2(1)
y = 2
(1, 2)
Should the inequality y > 2x - 1 be...
- drawn with a solid or dashed line?
- shaded above or below the boundary?
dashed line
shaded above
True or False: Mrs. Livermore has a cat
False, I have two daschunds (Oscar and Benny)
If the base graph of a parabola has been:
- translated 6 units up
- translated 4 units to the left
- reflected in the x-axis
- stretched vertically so that it is wider than before
Write an equation that could represent the function.
Answers will vary.
y = a(x+4)2 + 6 where a must be a negative number greater than -1 but less than 0
Solve.
0 = (x - 5)(x + 3)
x = 5, -3
Solve by Elimination.
y = x + 2
y = 2x2 - 1
y = 2x2 - 1
-(y = x + 2)
0 = 2x2 - x - 3
0 = (2x - 3)(x + 1)
x = 3/2, -1
y = (3/2) + 2
y = 7/2 or 3.5
y = -1 + 2
y = 1
(3/2, 7/2) and (-1, 1)
The solid boundary curve of an inequality is a parabola that opens up and has its vertex at (0, 4). If the graph is shaded below the boundary, write an inequality that could represent the graph.
Answers will vary.
y ≤ ax2 + 4 where a can be any positive value
True or False: Mrs. Livermore graduated from O'Leary