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Solve quadratic equations Determine number of solutions Choosing type: linear, quadratic, or exponential 10 Point 20 Points 30 Points 40 Points 50 Points 10 Point 20 Points 30 Points 40 Points 50 Points 30 Points 40 Points 50 Points Applications of Quadratic Equations Graphs of Quadratic Functions
Which way does the graph y = -6x open?
down
Where is the axis of symmetry for the graph of y = 2x 2 + 4?
X = 0
Where is the axis of symmetry for the graph of y = 4x 2 + 4x -2?
X = - 1/2
Find the axis of symmetry and vertex for the graph y = -3x 2 + 3x - 1
x = ½ (1/2, -1/4)
Find the vertex and axis of symmetry for y = 4 + 8x – 2x 2
X = 2 (2, 12)
Solve for x (x+2)(x-4) = 0
x= -2 or 4
Solve: x 2 + 3x + 2 = 0
x = -1 or -2
Solve: 2x 2 + 5x + 3 = 0
X = -1 or -1.5
Solve: 5x 2 – 68x = 192
X = 16 or -2.4
Solve and round to the nearest hundredth 2x 2 – 24x + 33 = 0
X = or 1.58
Suppose you throw a ball upward and the equation h = -16t 2 +30t + 6 models the path the ball takes where h is the height of the ball and t is time in seconds. After how many seconds will the ball hit the ground?
About 2.1 seconds
Suppose a rectangle has an area of 60 ft 2 and dimensions x and (x + 1). Find the dimensions of the rectangle to the nearest hundredth.
7.26 ft x 8.26 ft
A rectangle has a length of x. Its width is 3 feet longer than twice the length. Find the dimensions if its area is 80 ft 2. Round to the nearest tenth of a foot.
5.6 ft by 14.2 ft
An apartment rental agency uses the formula I = n – 50n 2 to find its monthly income I based on renting n apartments. Will the agencys monthly income ever reach $7000? Explain.
No, the discriminant is negative (300 2 – 4 (-50)(-1600) = -230,000)
For the equation x 2 + 2x + k = 0; find the value of k to the equation has one solution
k = 1
How many solutions does x 2 – 6x + 9 = 0 have?
One (discriminant = 0)
How many x-intercepts does x 2 – 2x – 3 = 0 have?
2 (discriminant = 16)
The function P = 3i 2 – 2i models the power P in an electric circuit with a current i. Can the power in this circuit ever be zero? If so, what is the value of i?
No, the discriminant is
How many zeros does the equation 2x 2 – 3x + 4 = 0 have?
None, the discriminant is -23.
Does the graph of the function cross the x- axis? y = 4x 2 + x - 5
Yes, twice. The discriminant is 81.
What type of equation do the points form? XY
Linear
What type of equation do the points form? XY
Quadratic
Find the type of equation and the equation the data forms XY
exponential, y = 5 (.4) x
Find the type of equation and the equation the data forms XY
Quadratic, y = 2.8x 2
Find the type of equation and the equation the data forms XY
Linear, Y = ½x + ½
Make your wager
A square pool has side length p. The border around the pool is 1 ft wide. The combined area of the border and the pool is 400 ft 2. Find the length and the area of the pool alone.
Length = 18 ft Area = 324 ft 2