I really need help on some sample work. Just need to check my answers:
1. Describe how the graph of y=-x^2+1 differs from y=x^2. Then find the axis of symmetry and the vertex
2. Graph the quadratic equation y=x^2+x-2. Identify the axis of symmetry and the vertex
3. A ball is thrown from the top of a 50-ft building with an upward velocity of 24 ft/s. When will it reach its maximum height? How far above the ground will it be? Use the equation
h(t)=-16+24+50
4. Solve the quadratic equation 3x^2=27
5. Solve the quadratic equation 2x^2-4x+1=0
6. How many solutions are in the equation
3x^2+4x-7=0
7. Solve by completing the square: A rectangular patio has a length of (x+6) m, a width of (x+8) m, and a total area of 400 m^2. Find the dimensions to the nearest tenth.
8. Find the radius of a circular lid with an area of 12in.^2
9. Solve the system of equations
{ y=x^2+9
y=6x
10. Solve the system of equations
{ y=4x+8
x^2+7x=20
4. 3x^2 = 27.
x^2 = 9,
X = 3, and -3.
1. Y = -x^2 + 1. Opens downward. y-int. = (0, 1).
h = Xv = -B/2A = 0/-2 = 0 = axis of symmetry.
k = Yv = -0^2 + 1 = 1. V(h, k) = V(0, 1).
Y = x^2. Opens upward. y-int. (0, 0).
h = Xv = -B/2A = 0/2 = 0 = axis of symmetry.
k = Yv = 0^2 = 0. V(0, 0).
2. Y = x^2 + x - 2.
-2 = -1 * 2. Sum = -1 + 2 = 1 = B.
(x-1)(x+2) = 0.
x - 1 = 0, X = 1.
x + 2 = 0, X = -2.
X-int. (1, 0), (-2, 0).
h = -B/2A = -1/2 = -0.5 = axis of symmetry.
k = (-0.5)^2 - 0.5 - 2 = -2.25. V(-0.5, -2.25).
Y-int. = 0^2 + 0 - 2 = -2. (0, -2), (-1, -2).
Graph: (-2, 0), (-1, -2), V(-0.5, -2.25), (0, -2), (1, 0).
3. V = Vo + g*t = 0.
24 + (-32)t = 0,
t = 0.75 s.
h = ho + Vo*t + 0.5g*t^2 = 50 + 24*0.75 + (-16) * 0.75^2 =
5. Use Quadratic Formula.
6. 3x^2 + 4x - 7 = 0.
h = Xv = -B/2A = -4/6 = -2/3.
k = Yv = 3(-2/3)^2 + 4(-2/3) - 7 =
If k is > 0, No real solution.
If k is = 0, 1 solution.
If k is < 0, 2 solutions.
8. pi * r^2 = 12.
3.14 * r^2 = 12,
r = ?
9. Y = x^2 + 9.
Y = 6x.
In Eq1, replace Y with 6x:
6x = x^2 + 9,
x^2 - 6x + 9 = 0,
Solve by factoring.