Quadratics
Graphing Vertex Form
Index
Image of Graph
Find x and y intercepts
Find Equation
Videos for Graph Quadratic Function in Vertex form
Video for Graphing with transformations
Word problem
Learning Goals
Summary of Vertex form
Vertex (h,k)
Axis of symmetry (x=h)
Optimal value y=k
a tells you the direction of opening as well as compression or stretch
h tells you horizontal translation
k tells you vertical translation
Step pattern : Starting from the vertex as "the first point" ...
OVER 1 (right or left) from the vertex point, UP 1² = 1 from the vertex point
OVER 2 (right or left) from the vertex point, UP 2² = 4 from the vertex point
OVER 3 (right or left) from the vertex point, UP 3² = 9 from the vertex point
Axis of Symmetry
Optimal value
What does a tells you about?
How to find vertex?
Vertex is (-4,-6) because +4 is h and it is changed into -4, K is -6 so this is the vertex (-4,-6).
The following image is of graph. You see which thing graph where.
How to find y-intercept if x set to 0.
Example: y=-1(x-3)²+4
y = -1(0-3)²+4(put x=0 in this equation).
=-1(-3)²+4
=-1*9+4
=-1*13
y=-13
To solve for x, set y=0.
y = a(x − h)² + k
0=2(x-4)²-50
0-50=2(x-4)²
50/2=2(x-4)²/2
√25=√(x-4)² [square root both side]
5=x-4
5+4=x
x=9
How to find an equation?
y = a(x − h)² + k
y=a(x+3)²-4 ------------ I put vertex here
6=a(2+3)²-4------------- I put x and y intercept here
6=a(25)-4
6=25a-4
6+4=25a
10/25=25a/25
2/5=a
∴y=2/5(x+3)²-4
The following Videos shows you how to graph Quadratic function in vertex form
Video discription
Video Discription
This video you see graphing using transformations and mapping notation
Video Discription
Word Problem using vertex form
a) Find maximum height of baseball?
b)At what time baseball reach its maximum height?
B) h=-2t²+6t
Let h=0
0= -4t+6
-6=-4t
-6/-4=t
1.5=t
A) -2(1.5)²+6(1.5)
h=-2*2.25+9
h=-4.5+9
h= 4.5
Learning Goals
2.Today I learn today how to find an equation.