Solving Quadratics
Solve:
x2-11x=-30
X=6
X=5
State the vertex, axis of symmetry, x and y- intercepts, Domain and Range
y=-2(x+3)2+2
Vertex:(-3,2)
aos: x=-3
y-intercept:-16
x- intercept:-4, -2
Domain: All real Numbers
Range: y is less than or equal to 2
y=x2-8x+10
y=(x-4)2-6
Vertex: (4,-6)
Solve the system
x2+10x+6y+8=13
2x+3y=7
(-3, 13/3)
A rainbows path follows the quadratic r(x)=-1/30(x+12)(x-12). where x is the horizontal distance in miles and r(x) is the height in miles. What is the distance between the two places where it appears to hit the ground?
24 miles
Solve:
m2=7m
m=0
m=7
State the vertex, axis of symmetry, x and y- intercepts, Domain and Range
y=4(x+2)(X+4)
Vertex:(-3,-4)
aos: x=-3
y-intercept: 32
x- intercept:-4, -2
Domain: All real Numbers
Range: y is greater than or equal to -4
Write in vertex form. And state the vertex.
y=-3x2+12x-7
y=-3(x-2)2+5
Vertex: (2,5)
Solve the system:
f(x)=3x2-7x+4
g(x)=5x+4
A rectangle has an area of of 30in2. The length is 1 unit shorter than the width. Find the dimensions of the rectangle.
6inx5in
Solve:
0=4(x+3)2-1
x=-2.5
x=-3.5
Graph y=(x+3)2+1 over the domain (-5,-3] U (-2, 0]
SEE graph
End points should be:
(-5, 5), (-3,1), (-2,2), and (0,10)
Write in vertex form and state the vertex.
f(x)=2x2+4x-5
f(x)=2(x+1)2-7
(-1, -7)
Solve the system:
x2-14x+3y-4=5
2x-y=8
(11, 14) and (-3, -14)
Write a quadratic in intercept for whose graph has x-intercepts at -3 and 9 and passes through the point (-6,-7).
y=-7/45(x+3)(x-9)
Solve:
0=4x2-11x+6
x=2
x=3/4
Graph y=-x(x+6) over the domain [-7,-5) U (-1,2]
See graph
Endpoints will be at:
(-7, -7), (-5, 5), (-1, 5), and (2, -16)
Write in vertex form and state the vertex:
y=-2x2+6x-3
y=-2(x-3/2)2+3/2
Vertex: (3/2, 3/2)
Write a system of equations that could be used to write a quadratic function in standard form for a parabola passing through (2,6), (3,5) and (-4, 25)
4a+2b+c=6
9a+3b+c=5
16a-4b+c=25
A frisbee throw can be modeled by y=-0.02(x+6)(x-52.4). How long was the throw if x is the frisbees horizontal distance and y is the vertical distance, both in feet? What is the maximum height of the frisbee?
52.4 feet
17.05 feet
Solve:
2x2-3x+2=0
(3+/-i Root 7)/4
graph y>.25(x+2)2+3
See graph
Should be a dotted line shaded on the inside
Write in vertex form. What is the vertex?
f(x)=2x2-18x+4
2(x-9/2)2-73/2
Vertex:(9/2, -73/2)
Write a system of equations that could be used to write a quadratic function in standard form for a parabola passing through (-3, -2), (6, -4) and (9, 10)
9a-3b+c=-2
36a+6b+c=-4
81a+9b+c=10
AN object is launched directly upward at 176 feet per second from a platform that is 45 feet high. What is the maximum height? What time will it attain that height?
Use: h=-16t2+v0t+h0
Maximum height is 529 feet
It will take 5.5 seconds to get there.