Quadratic Forms
y=(x+5)(x+1)
standard form, factored form or vertex form?
factored form
Write a quadratic equation in standard form that has a y-intercept of 20.
answers vary
y=ax2+bx+20
What is the y-intercept?
(0,0)
Find g(x), where g(x) is the translation 3 units up of f(x)=x2.
f(x)=x2 + 3
Find the product of 5(2x+1). Simplify your answer.
10x+5
g(x)=x2 -2x
What is the y-intercept of g(x)?
(0,0)
Write a quadratic equation in factored form that has x-intercepts (-5,0) and (1,0).
y=(x+5)(x-1)
What are the coordinates of the vertex?
x| -4 -3 -2 -1 0 1 2
y| 8 3 0 -1 0 3 8
(-1, -1)
Find g(x), where g(x) is a shift 7 units left of f(x)=x2.
g(x)=(x+7)2
Find the product of 2x(4x+3). Simplify your answer.
8x2 +6x
f(x)=(x-2)(x-6)
What are the x-intercepts of f(x)?
(6,0) and (2,0)
Write a quadratic equation in vertex form that has a vertex of (-1,2).
y=(x+1)2+2
What is the axis of symmetry?
x=0
Find g(x), where g(x) is the reflection across the x-axis of f(x)=x2.
f(x)=-x2
Find the product of (x+3)(x+4). Simplify your answer.
x2 +7x+12
h(x)=(x-4)2 -4
What is the vertex of h(x)?
(4, -4)
Write a quadratic equation that produces the following table:
x y
0 10
1 5
2 2
3 1
4 2
5 5
y=x2 -6x+10
or
y=(x-3)2+1
What is the minimum?
-4
If f(x)=x2, find g(x) where it represents a shift of the graph of f(x) 5 units to the left and 2 units down?
g(x)=(x+5)2 -2
Find the product of (2x-1)(3x-1). Simplify your answer.
6x2 -5x+1
A football player throws a football. Function h given by h(t)=6+75t-16t2
describes the football's height in feet, t seconds after it's thrown.
How long was the football in the air?
~4.8 seconds
Study the pattern of squares. If S represents the number of small squares in the pattern as a function of n, the step number, then write an expression that could define S.
n2+2
What is the minimum of
f(x)=(x-3)2 -7?
-7
If f(x)=|x|, find g(x) where it represents a shift of the graph of f(x) 2 units to the right?
g(x)=|x-2|
Find the product of (x-3)2. Simplify your answer.
x2 -6x+9