1. Quadratic Functions & Models
Chapter 4.10
Quadratic Functions & Models
p , 17-23, 26, 27
#33 “Philosophy is a game with objectives and no rules. Mathematics is a game with rules and no objectives.”
~Author Unknown

2. Quadratic Properties

3. Vertex Form Vocab h is the horizontal shift k is the vertical shift
a determines up/down orientation and fat/skinny parabolas.
Vertex is at the point (h,k)

4. Intercept Form x-intercepts are at (p,0) & (q,0)
Axis of symmetry is halfway between p&q.
a determines up/down orientation and fat/skinny parabolas.

5. Complete the Square to Solve a Quadratic
From this we see our vertex is (-6,-1)
From this we see P and Q are -5 and -7

6. Using all that info we can start to work these problems backwards
Just like in algebra one, given a slope was 3 and the line passes through the point (4,2) what is the equation of the line.

7. Vertex Form
When given the vertex and a point on the graph put the equation in vertex form. h k x y
Substitute in the h & k
Substitute in the x & y
Solve for a
Rewrite the equation using the values of h,k & a

8. Vertex Form
When given the vertex and a point on the graph put the equation in vertex form. h k x y
Substitute in the h & k
Substitute in the x & y
Solve for a
Rewrite the equation using the values of h,k & a

9. Vertex Form Substitute in the h & k Substitute in the x & y
Solve for a
Rewrite the equation using the values of h,k & a

10. Intercept Form
When given the intercepts and a point on the graph put the equation in intercept form. p q x y
Substitute in the p & q values from the intercepts.
Substitute in the x & y values from the point.
Solve for a
Rewrite the equation using the values of p,q & a

11. Intercept Form
When given the intercepts and a point on the graph put the equation in intercept form. q p x y
Substitute in the p & q values from the intercepts.
Substitute in the x & y values from the point.
Solve for a
Rewrite the equation using the values of p,q & a

12. Intercept Form
When given the intercepts and a point on the graph put the equation in intercept form.
Substitute in the p & q values from the intercepts.
Substitute in the x & y values from the point.
Solve for a
Rewrite the equation using the values of p,q & a

13. Assignment
p , 17-23, 26, 27