Finding Key Features with Factored Form
On the 6th day of Quadratics, my teacher gave to me… nothing about geese…
Learning Goals
By the end of the lesson I will be able to:
Review
Expand and simplify: (3x - 3)(2x + 4)
(3x - 3)
(2x + 4)
3x
-3
2x
4
6x2
-6x
12x
-12
= 6x2 - 6x + 12x - 12
= 6x2 + 6x - 12
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Review
F - First O - Outside I - Inside L - Last
y = (2x + 1)(x - 3)
2x2
-6x
x
-3
y = (2x + 1)(x - 3)
= 2x2 - 6x + x - 3
-5x
= x2 - 5x - 3
Key Features
| Green | Blue | Red |
Zeros / x-intercepts | | | |
Axis of Symmetry | | | |
Find the Link
If we know the x-intercepts, how can we find the axis of symmetry?
| Green | Blue | Red |
Zeros / x-intercepts | -10, -6 | -4, 2 | 4, 9 |
Axis of Symmetry | x = -8 | x = -1 | x = 6.5 |
Gallery Walk
Move around the room and collect your data!
You should be filling out the chart on your worksheet.
This one’s for you Taylor...
Equations
y = (x + 1)(x + 2)
y = x2 + 3x + 2
You asked me to put things in the titles again
Equations
y = (x - 2)(x - 5)
y = x2 - 7x + 10
Don’t say I never did nothin’ for ya
Equations
y = (x - 4)(x + 1)
y = x2 - 3x - 4
OMG LOOK BEHIND YOU!
Equations
y = (x + 0)(x + 3)
y = x2 + 3x
HA! Gotcha! … Probably…
Equations
y = (x + 2)(x + 3)
y = x2 + 5x + 6
Hey, I have a question for you:
Equations
y = (x + 1)(x - 1)
y = x2 - 1
Does this paper smell like bacon?
Equations
y = (x + 2)(x - 4)
y = x2 - 2x - 8
‘cuz I cooked bacon just before I made the slides...
Equations
y = (x - 1)(x - 3)
y = x2 - 4x + 3
So I figured, since my house smells like bacon...
Equations
y = (x + 1)(x + 3)
y = x2 + 4x + 3
This has to smell like bacon too, right? Weird...
Equations
y = (x - 2)(x - 3)
y = x2 - 5x + 6
Factored Form and zeros/Roots
How can you determine the zeros / roots / x‐intercepts of a parabola from its factored form equation?
Standard Form and the Y-Intercept
How can you determine the y‐intercept of a parabola from its standard form equation?
Factored Form and the y-Intercept
How can you determine the y‐intercept of a parabola from its factored form equation?
Factored form and Graphing
How can we graph a parabola given its factored form equation?
1. Plot the zeros.
2. Determine the axis of symmetry by adding the zeros together and then dividing by 2.
3. Draw the axis of symmetry on your graph.
4. Determine the y-intercept by multiplying the zeros together.
5. Plot the y-intercept on your graph.
6. Plot one additional point by "reflecting" the y-intercept across the axis of symmetry.