Quadratic Characteristics
f(x)=-x2-x+6
Find the Domain
(-inf, inf)
Convert the following to intercept form (Hint: Factor the GCF and keep it out front)
f(x)=3x2-15x+18
f(x)=3(x-3)(x-2)
Brian throws a tv off the top of a cliff after watching Georgia and the Falcons lose. The situation can be modeled by the following equation where t represents time in seconds, and y represents height above ground in feet.
y=-16t2+24t+160
What is the y-int mean in context?
Brian throws the TV from a height of 160 feet.
Find the solution(s) to the equation?
25x2=36
x=-6/5
x=6/5
Find the AROC over the interval [-2,1] for the following function:
y=2x2+5x-4
You can use Desmos
9/3 = 3
f(x)=-x2-x+6
What is the Range?
(-inf,6.25]
Write f(x)=x2 - 4x - 12 in intercept form.
f(x)=(x-6)(x+2)
Brian throws a tv off the top of a cliff after watching Georgia and the Falcons lose. The situation can be modeled by the following equation where t represents time in seconds, and y represents height above ground in feet.
y=-16t2+24t+160
What is the maximum height of the TV?
169 feet
What value(s) of x make the equation true?
(x-4)2=18
x=4+3sqrt2
x=4-3sqrt2
The profit, P (in thousands of dollars), that a company makes selling video games is a quadratic function of the price of the video game, x.
P(x)=-3(x-25)2+600
What is the characteristics that can be found easily from the equation? What does it mean in context?
The vertex, it represents that if the company sells the game for $25 , they will make a maximum profit of $600,000.
f(x)=-x2-x+6
Find the vertex and axis of symmetry.
(-0.5,6.25); x=-0.5
Write f(x)=(4x - 1)(x + 2) in standard form.
f(x)=4x2+7x-2
Brian throws a tv off the top of a cliff after watching Georgia and the Falcons lose. The situation can be modeled by the following equation where t represents time in seconds, and y represents height above ground in feet.
y=-16t2+24t+160
After how many seconds does the TV reach it's maximum height?
0.75 second
The length and width of a rectangle are consecutive integers. The area of the rectangle is 156 square feet. Write an equation to find the length and width of the rectangle.
x(x+1)=156
f(x)=-x2-x+6
Find the end behavior.
As x->inf, f(x)->-inf
f(x)=-x2-x+6
Find the interval of increase.
(-inf,-0.5)
Write y=2x2 + 5x + 3 in intercept form.
y=(2x+3)(x+1)
Brian throws a tv off the top of a cliff after watching Georgia and the Falcons lose. The situation can be modeled by the following equation where t represents time in seconds, and y represents height above ground in feet.
y=-16t2+24t+160
What is the positive x-intercept and what does it mean in context?
(4,0), The TV will hit the ground after 4 seconds.
Solve the equation for x:
2x2-12x-21=11
x=-2,8
3, 8, 15
f(n)=n2+2n
f(x)=-x2-x+6
Find the interval of negative y-values.
(-inf,-3)U(2,inf)
What is a common factor when the expressions below are factored?
x2-9x-10 and x2+11x+10
(x+1)
Brian throws a tv off the top of a cliff after watching Georgia and the Falcons lose. The situation can be modeled by the following equation where t represents time in seconds, and y represents height above ground in feet.
y=-16t2+24t+160
When will the object be back it's initial height?
1.5 seconds
The length of a rectangular poster is 10 more inches than three times its width. The area of the poster is 88 square inches. Solve for the dimensions (length and width) of the poster.
Width: 4 in
Length: 22 in
Write an equation of a parabola in standard form that passes through the points (-11,0)(-3,0).
y=x2+14x+33