Introduction to Quadratics
Presentation
•
Mathematics
•
11th Grade
•
Practice Problem
•
Hard
Connie Schaef
Used 12+ times
FREE Resource
12 Slides • 0 Questions
1
2
Standard Form | Vertex Form |
|---|---|
y = ax2 + bx + c | y = a(x - h)2 + k |
f(x) = ax2 + bx + c | f(x) = a(x - h)2 + k |
3
Graph of parent function
parabola
vertex at origin
opens up
4
vertex
axis of symmetry
x-intercepts
y-intercept
domain
range
5
6
let x = 0
y = ax2 + bx + c
y = a(0)2 + b(0) + c
y = 0 + 0 + c
y = c
Therefore y-intercept = (0, c)
7
Factoring
Zero Product Rule
Quadratic Formula
Completing the Square
y = a(x - h)2 + k
8
aka..... (roots, solution, zeros)
Since quadratic are x2 the "2" in the exponent tells you it will always have 2 answers
Although the answer could be
2 distinct answers
multiple root (same answer appears twice)
2 imaginary root
9
Will always go through the VERTEX (h, k)
Will always be a vertical line
Will always be x = h
10
let x = 0
y = a(x - h)2 + k
y = a(0 - h)2 + k
y = ah2 + k
11
let y = 0
y = a(x - h)2 + k
square root method
Put in standard form and use standard form method
12
make a T- table and substitute number
y = x2 + 3x + 2
x | x2 + 3x + 2 | y |
|---|---|---|
-2 | (-2)2 + 3(-2) + 2 = 0 | 0 |
-1 | (-1)2 + 3(-1) + 2 = 0 | 0 |
0 | (0)2 + 3(0) + 2 = 2 | 2 |
1 | (1)2 + 3(1) + 2 = 6 | 6 |
2 | (2)2 + 3(2) + 2 = 0 | 12 |
Rules when making a T-table
1) must use at least 5 point
2) must have at least 2
y-values that repeat
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