Quadratic Equations
What is the vertex form of quadratic functions?
f(x) = a (x - h)2 + k
24
16
Point slope form
Slope-intercept form
Standard Form
Define: Expression
An expression in math is a statement having minimum of two numbers, or variables, or both and an operator connecting them
Add the polynomials below:
(2x2 - 5x + 8) + (x2 - 3x + 4)
3x2 - 8x + 12
b2 + 8 b + 7
(b+7), (b+1)
What does (h,k) from the vertex form give you?
the vertex!
What is the formula for exponential growth functions?
f(x) = a (1+r)^t
What is the slope for a line that is perpendicular to the linear equation below?
y = -5/2x + 4
2/5
Define: Equation
Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
Multiply the polynomials below:
(x - 2)(x + 7)
x2 + 5x - 14
n2-11n+10
(n-10) (n-1)
If a has a value of -2, what two things are affected from the parent function f(x) = x2
The graph is vertically stretched (narrower) by a factor of 2.
The graph is reflected over the x-axis (opens down)
A football is thrown into the air 50 feet. The height of the ball, in meters, can be calculated by using the formula below.
h(t) = -16t2 + 144t - 20
In the formula, [t] is the total elapsed time, in seconds, since the ball was thrown into the air.
What is the height of the ball after 5 seconds?
300 ft
What is the slope of a linear function that is a vertical line?
Undefined
Variable
In simple words, a variable is a quantity that can be changed and is not fixed. Variables are essential as they form a major algebra component.
Simplify the expression below:
(3k3 - 2k2 + 1) - (-5k3 + k2 - 5)
(8k3 - 3k2 + 6)
m2+2m-24
(m+6) (m-4)
Describe the transformations that occur: *Hint: There are 3*
f(x) = - (x - 4)2 + 2
Reflects over x-axis
Shifts right 4 units
Shifts up 2 units
DOUBLE JEOPARDY: What is the y - intercept and axis of symmetry of the graph shown? (in your files VELEZ)
y intercept: (0,5)
Axis of symmetry: x = 2
What is the slope of the linear function that is shown? (picture in files)
1/2
Constant
In its simplest definition, a constant is a fixed value, such as the number 5. It does not change with respect to the variables in an expression or equation.
Simplify the expression below:
2k(k2 + 3k - 6)
2k3 + 6k2 - 12k
Factor the expression below:
x2 - 144
(x + 12)(x - 12)
What are the solutions (x-intercepts) of the quadratic equation below?
x2 - 16x + 39
x = 13 , x = 3
VELEZ invested $5000 in a Stock account. The formula below shows the amount of money, [A] , that will be in his account at the end of [t] years.
A =5000(1 + r)^t
In the formula, r is the interest rate, expressed as a decimal. VELEZ′s account has an interest rate of 8%.
What amount of money will be in VELEZ′s Stock account at the end of 10 years?
$10,794.62
What is the y-intercept of the function below? (Express your answer as a coordinate point).
y + 4 = 2x - 5
(0,-9)
Polynomial
A mathematical expression is a number represented by variables, constants, and the mathematical operations performed on them.
FINAL JEOPARDY: Does the sequence below represent a linear function, quadratic function, exponential function, or none?
3, 9, 27, 81...
Exponential
Factor out the GCF from the expression below:
(3x2y2 + 6xy2 - 9x4y)
3xy(xy + 2y - 3x3)