Describing Quadratics
Does the Following Quadratic Open UP or DOWN? y=-3x2+4x-6
What is DOWN.
This is the meaning of the acronym: F.O.I.L.
What is Firsts, Outsides, Insides, Lasts?
Find the Vertex.
y=x2+2x-3
(-1,-4)
What are the solutions of a quadratic function?
x-intercepts (or zeroes), roots
What is the name for the shape of a quadratic graph?
Parabola
If a parabola opens DOWN, it is said to have a minimum value. TRUE or FALSE?
FALSE
Multiply. (x+4)(x-2)
x^2+2x-8
This is the y-intercept of y=x^2-2x-15
hint: when x=0
What is -15
Rewrite in standard form. y=(x+2)(x+6)
y=x^2+8x+12
What is standard form of a quadratic function?
y=ax^2+bx+c
If a Parabola is OPEN UPWARD and has a minimum value Y = 4; What is it's Range?
[4, +Infinity)
Multiply. (x-3)(x+5)
x^2+2x-15
Name 2 key features of the graph of y=x2-4x+7
Vertex (2, 3)
Opens up
y-intercept (0,7)
Axis of Symmetry x=2
y=ax^2+bx+c
Name one key feature of the graph controlled by "a."
Whether it opens up or down
the width of the parabola
In a graph of a kicked ball, what key feature represents the TIME the ball reached its highest point?
the x value of the vertex
If a Parabola is open DOWNWARD and has x-intercepts at 0 and 6, what is its Axis of Symmetry?
x = 3
Multiply. (-3x-5)(-6x+7)
18x^2+9x-35
Find the vertex. y=-4x2+24x-35
(3, 1)
y=ax^2+bx+c
What point on the graph does "c" correspond with?
The y-intercept
In a graph of a kicked ball, what key feature represents the maximum HEIGHT the ball achieved?
the y value of the vertex
How do I find the vertex if I know the Axis of Symmetry?
Plug in X to find Y
Multiply. -(x+3)(4x-5)
-4x^2-7x+15
Find the Axis of Symmetry: y=-1/2x2-4x+4
x = 4
Describe an example of the graph of a quadratic function that has NO SOLUTION.
vertex is in the 1st or 2nd quadrant and the parabola opens UP ---OR---- vertex is in the 3rd or 4th quadrant and the parabola opens DOWN.
In a graph of a kicked ball, what key feature represents the TIME the ball hit the ground?
The x-intercept