Definitions
What is an x-intercept?
When y = 0, zeros, when a graph crosses the x -axis
What is the Quadratic Formula?
x = (-b +- sqrt(b2 - 4ac))/2a
Graph the line y = -2x + 3
b = 3 and m = -2
What are 3/4 reasons that an expressing is a nonmonomial?
Negative Exponent
Multiple Terms
Variable in the Denominator
Variable in the Exponent
Factor the quadratic expression: x2 - 13x - 48
(x + 3)(x - 16)
What makes a function a quadratic equation?
When completing the square, what are the four steps?
1) Multiple by the leading coefficient
2) Add b2/4a to both sides
3) Square root 1st and 3rd
4) Solve using the square root property
Solve the System of Equations by Graphing
y = -1/2x + 3
x + 2y = 6
Infinitely Many Solutions
Find the product: (12x3yz3)(-2xy)(3yz4)
-72x4y3z7
Factor the Quadratic: 2x2 -6x - 20 = 0
(2x + 4)(x - 5)
What is a maximum or minimum value?
The y-coordinate of a vertex
Rewrite the quadratic function in intercept form:
f(x) = 3x2 - 3x - 90
f(x) = 3(x + 5)(x - 6)
Graph the Function and determine the zeros
y = 4x2 + 2x -6
Zeros = -1.5 and 1
Degree = 3
Leading Coefficient = - 3
Classification = Trinomial
Factor the Quadratic: 25x4 + 15x3 + 5x2
5x2(5x2 + 3x + 1)
What is the zero product property?
When factors are set = to zero to solve for the x-intercepts
Determine the vertex and x-intercepts from this quadratic function using any method.
h(x) = 3x2 - 6x - 72
x -intercepts: 4 and -6
Vertex (1, -75)
Solve the System of Inequalities by Graphing:
y > 2/3x - 1
y < -4x + 1
See Desmos
Find the Product: (3x - 12)(-2x + 4)
-6x2 + 36x - 48
Use the Square Root Property to Solve
-12(x2 + 3) -10 = -58
x = -1 and 1
What is the simplest radical form?
When a radical is simplified as much as possible
i.e. Sqrt (125) = 5sqrt5
Rewrite the quadratic function from standard form to vertex form:
g(x) = 4x2 +32x -16
g(x) = 4(x + 4)2 - 48
Write the System of Inequalities for this graph
Answer
Find the product: (12x -3)2(-4x + 1)
-576x3 + 432x2 - 108x + 9
6x2 - 23x + 20
(2x - 5)(3x - 4)