4.1: Graphing Quadratic Functions
The equation y=-2x2-8x-5 has a vertex of (-2,3). Identify the domain and range.
Domain: all real numbers
Range: y is less than or equal to 3
If s(t)=-16t2+5t+10, what is the initial height?
10 ft
Factor 2x2-98.
2(x-7)(x+7)
Simplify.
(3-2i)-(-6-3i)
9+i
Identify the axis of symmetry for
f(x)=2x2-8x+5.
x=2
If s(t)=-4.9t2+20, what is the initial velocity?
Factor 15x2+7x-2.
(5x-1)(3x+2)
Solve.
3x2=-48
x=4i, -4i
Determine the min/max and find the value for
f(x)=5-4x-2x2.
Max: 7
What is another name for zeros of the function?
Roots
Solve by factoring.
10x2+25x=15
x=-3, 1/2
Simplify.
(2-4i)(5+6i)
34-8i
Write a quadratic equation that passes through the point (4,11) and has a vertex at (2,-1).
y=3(x-2)2-1
When will a dropped object hit the ground if its initial height is 40ft? Round your answer to the nearest hundredths.
1.58 seconds
Solve by factoring.
-7x2+6x=20x3
x=0, 2/5, -3/4
Simplify.
3-4i
2i
(-3i-4)/2
Last year, 300 people attended the winter play. The ticket price was $8. The advisor estimates that 20 fewer people will attend for each $1 increase in price. What ticket price would give the greatest income for the Drama Club?
$11.50
If an object is thrown with an initial velocity of 26 m/s and starts at an initial height of 5 meters, how long will the object be in the air before it reaches the ground? Round your answer to the nearest hundredths.
5.49 seconds
Write an equation in standard form with the given roots.
-4/7 and 3/8
56x2+11x-12=0
Simplify.
5i
2-i
2i-1