Day 1.Vertex Form.Factored Form.17.notebook
February 17, 2017
Topic: Parabolas
Aim: How do we write the equation of a quadratic in
Vertex form and General form? Do Now: Find the y-intercept(when x=0) and zeros(when
y=0) of both equations below. What do you realize?
2) y = x2 ­ 4x + 3
1) y =(x ­ 2)2 ­ 1
Students please note
changes in
red....change on your
handout!
What is different about each of these equations?
Dec 18­8:50 AM
Quadratic Equations
General Form: y = ax2 + bx + c
f(x) = ax2 + bx + c
Vertex Form: y = a(x - h)2 + k : vertex at (h, k)
f(x)=a(x - h)2 + k
*The value of a in both forms shows gives us an
idea of the scale factor.
Recall: When a>0--> concave up
When a<0-->concave down
When a>1 the parabola will be more narrow
When 0<a<1 the parabola will be more wide
Dec 18­1:08 PM
1
Day 1.Vertex Form.Factored Form.17.notebook
February 17, 2017
Sketch using the y-intercept; x intercept(s); and vertex
without a calculator.
1)
f(x) = x2 ­ 2x ­ 3
Dec 18­1:13 PM
2) y = 2x2 + 12x + 18
Dec 21­9:55 AM
2
Day 1.Vertex Form.Factored Form.17.notebook
February 17, 2017
General Form
f(x) = ax2 +bx+c
*Easily identifies y­intercept (simply the c value) and direction
Factored Form
f(x)=a(x­r1)(x­r2)
*Easily identify's x­intercepts/roots/
solutions (r1 & r2) and direction
Vertex Form
f(x)=a(x­h)2+k
*Easily identify's vertex(h,k) and direction
Dec 21­9:59 AM
Place each of the following equations in vertex form
to sketch. Identify if the roots are real or imaginary
from the sketch.
2 5) y = x + 4x ­ 1
Dec 21­9:50 AM
3
Day 1.Vertex Form.Factored Form.17.notebook
3)
February 17, 2017
f(x) = x2+12x + 40
Dec 18­1:13 PM
4)
y = ­5x2 ­ 20x + 35
Dec 18­1:13 PM
4