Graphing Quadratics
What are the 4 names for the answers to Quadratics?
x-intercepts, solutions, zeros, roots
Solve:
x^2-36=0
x = 6 and x= -6
Solve:
x^2+5x-24=0
x=-8, x = 3
Solve
-3x^2-5x+2=0
x=-2 and x = 1/3
What is the maximum height of a rocket whose flight can be modeled by:
f(x) = -16x^2+25x ?
x = 9.76 feet
What is the y-intercept of
y=x^2 - 5x + 6
(0,6)
Solve:
-3x(4x - 5)=0
x =0 and x = 5/4 (or 1.25)
Solve:
4x^2-17x+4=0
x = 4, and x= 1/4
Solve:
x^2+4x+3=0
x = -1 and x = -3
How long does it take for a rocket to reach the ground again if it's flight is modeled by:
f(x)=-16x^2+100x?
6.25 secs
What is the vertex of
x^2-5x+6
(2.5, -0.25)
Solve:
10x^2-3x=0
x = 0, x = 3/10
Solve:
2x^2-7x+3=0
x = 1/2, x=3
Solve:
x^2-4x=-1
x = 3.73 and x = 0.26
What is the height of a rocket at 5 sec? Use the equation:
f(x)=-16x^2+240x+15
815 feet
Does this parabola have a max or a min and WHY?
2x^2 - 7x - 5
Min because the "a" is positive
Solve:
x^2-30x-59=5
x = -2, x = 32
Solve:
4x^2+24x+36=0
x = -3
Solve:
9x^2-6x-4 = -5
x = 1/3
How long does it take this rocket to reach its maximum height? Use
-16x^2+120x+2
3.76 sec
What is the Axis of Symmetry for
x^2 + 4x + 4
x=-2
Solve:
3x^2-7=10x
x= -0.59 and x = 3.92
Solve:
-2x^2+12x-16=0
x = 2, x = 4
Solve:
2x^2-7x-13=-10
x=3.88 and x = -0.38
How long does it take this rocket to reach the ground again?
Use:
f(x)=-16x^2+120x+2
7.5 sec