Types of Forms
What is the standard form of a quadratic function?
f(x) = ax² + bx + c
What shape does a quadratic graph always make and how do you spell it?
Parabola
P-A-R-A-B-O-L-A
In f(x) = (x - 2)², what happens to the graph?
What are the roots of f(x) = (x - 1)(x + 3)?
x=1 or x=-3
f(x) = x² + 2x + 1 a quadratic?
Yes
Convert f(x) = (x - 3)(x + 5) to standard form
f(x) = x² + 2x - 15
In f(x) = x² - 4x + 1, what direction does the parabola open?
Up
How does f(x) = -x² compare to f(x) = x²?
It opens downward
Solve x² - 9 = 0
x = ±3
f(x) = x³ - x² + 2 a quadratic?
No
Identify the form of f(x) = 2(x - 1)² + 4
f(x) = (x - 3)²
What is the vertex of f(x) = (x + 2)² - 9?
(-2, -9)
What does the "3" do in f(x) = 3x²?
It makes the graph narrower
Use the quadratic formula to solve x² - 4x - 5 = 0
x=5 or x=-1
What makes a function quadratic?
Highest exponent on x is 2
Rewrite f(x) = x² - 6x + 9 in vertex form
f(x) = (x - 3)²
For f(x) = -x² + 6x - 8, find the axis of symmetry
x=3
In f(x) = (x + 1)² - 5, what transformation occurred?
1 unit left, 5 units down
How many real roots does x² + 4x + 8 have?
0
f(x) = (2x - 1)(x + 4) a quadratic function?
Yes
Given f(x) = -2x² + 8x - 3, convert to factored form
f(x) = -2(x - 3)(x - 0.5)
Identify the y-intercept of f(x) = 2(x - 1)(x + 4)
f(0) = -8
Describe the full transformation of f(x) = -2(x - 4)² + 7.
4 units right, 7 units up, reflected, and vertically stretched by 2
Solve 2x² + 7x + 3 = 0.
x=-1/2 or x=-3
Is y = 7 a quadratic function? If no, what is it?
No
It's a constant function