Solving Equations
Graphing Equations
Deriving the Quadratic Formula (must be done in order!)
100
How many solutions are there for the equation
2x^2 - 6x + 7 = 0
None
100
Does the graph
y = 3x^2 + 4x + 7
have a minimum or maximum value?
Minimum
100
Turn
ax^2 + bx + c
into the quadratic formula. The first step is to divide both sides by a. What is the next step?
Subtract c/a from both sides
200
Leave answer in radical form:
x^2 - 10x = 1
x = 5 +- sqrt(26)
200
What is the vertex of
y = 2x^2
(0,0)
200
The next step is to complete the square. What is the formula for a trinomial square (assuming all values are positive)?
a^2 + 2ab + b^2
300
(4x - 5)^2 = 9
x = 1/2 and x = 2
300
What are the x-intercepts of
y = 3x^2 - 27
(3, 0) and (-3, 0)
300
What is half of the x-coefficient in
x^2 + (bx)/a = -c/a
b/(2a)
400
(x-3)^2 - 3(x - 3) - 4 = 0
x = 7 and x = 2
400
Which of the following functions could be represented by the graph?
g(x) and p(x)
400
Complete the square
x^2 + (bx)/a = -c/a
x^2 + (bx)/a + b^2/(4a^2) = b^2/(4a^2) - c/a
500
The function below represents the height of a model rocket as it travels x seconds through the air. Find the rocket's highest point and how long it takes to land.
h = -16x^2 + 128x
256 feet
8 seconds
500
What is the vertex of
y = -6x^2 + 24x - 20
(2, 4)
500
Finish solving for x
(x + b/(2a))^2 = b^2/(4a^2) - c/a
(x + b/(2a))^2 = b^2/(4a^2) - (4ac)/(4a^2)
(x + b/(2a))^2 = (b^2 - 4ac)/(4a^2)
x + b/(2a) = +-sqrt(b^2 - 4ac)/(2a)
x = -b +-sqrt(b^2 - 4ac)/(2a)