Basic Concepts
What is the name of a graph for a quadratic function?
A parabola (U-shape)
Before factoring, you should determine if the equation has....
A GCF (greatest common factor)
"a" determines if the graph.....
Opens up/Opens down
"|a|" determines if the transformation of the graph......
Dilation - whether the graph vertically stretches "skinny" OR vertically compresses "wide"
How do you find the maximum height and time of a graph?
The vertex
What is the standard form of a quadratic equation?
y = ax2 + bx + c
Factor.
x2 − 16x + 63
(x - 9)(x - 7)
The vertex of a graph determines...
If the graph has a maximum or minimum.
In vertex form of a quadratic equation, in a transformation, the "h" and "k" represents how the graph moves...
"h" moves the graph horizontally (left/right)
"k" moves the graph vertically (up/down)
How do you find the time of a parabolic equation when it is in standard form?
Use x = -b / 2a
This will give you the time.
What is the vertex form of a quadratic equation?
y = a(x - h)2 + k
Factor.
(x2 - 81) = y
y = (x + 9)(x - 9)
How do you find the y-intercept of a quadratic graph?
In any form, plus in x = 0 into the equation and solve for y.
If the parent function x2 is vertically stretched by a factor of 3, translated 7 units to the right, then translated 3 units up, write the resulting function in vertex form.
y = 3(x - 7)2 + 3
How do you find the maximum height of a parabolic equation?
Substitute the x-value from the axis of symmetry into the original equation, then solve.
What is the factored form of a quadratic equation?
y = a(x - r1)(x - r2)
Factor.
y = 5p2 − p − 18
y = (5p + 9)(p - 2)
Find the axis of symmetry for the equation y = -x2 + 6x - 4
x = 3
If the parent function x2 is vertically compressed by a factor of 1/2, translated 9 units to the left, then translated 4 units down, write the resulting function in vertex form.
y = 1/2(x + 9)2 - 4
Find the maximum height of the following equation, where t is measured in seconds and height is measured in feet. h(t) = -16t2 +64t +80
t = 2
h(t) = 144 ft
How do you find the vertex of a quadratic equation in standard form?
Factor.
28n4 + 16n3− 80n2
4n2(7n - 10)(n + 2)
If the parent function x2, describe the following transformation in words. y = 7/5(x+2)2 + 7
The graph is vertically stretched by a factor of 7/5. It is translated 2 units to the left and translated 7 units up.
If the parent function x2. Describe the following transformation in words. y = 1/5(x-4)2 +3.
The graph is vertically compressed by a factor of 1/5. Translated horizontally 4 units to the right and translated vertically 3 units up.
Draw a graph representing the following parabolic equation if the time is between 0 and 8 seconds. h(t) = -16t2 +128t
The Vertex: (4, 256)