Chapter 4 10 Quadratic Functions Models p 312

Vertex Form Vocab • h is the horizontal shift • k is the vertical

Intercept Form • x-intercepts are at (p, 0) & (q, 0) • Axis of

Complete the Square to Solve a Quadratic From this we see our vertex is

Using all that info we can start to work these problems backwards Just like

Vertex Form When given the vertex and a point on the graph put the

Vertex Form 1. Substitute in the h & k 2. Substitute in the x

Intercept Form When given the intercepts and a point on the graph put the

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Chapter 4. 10 Quadratic Functions & Models p 312 3 -9, 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

Quadratic Properties

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)

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.

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

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.

Vertex Form When given the vertex and a point on the graph put the equation in vertex form. 1. Substitute in the h & k 2. Substitute in the x & y 3. Solve for a 4. Rewrite the equation using the values of h, k &a h k x y

Vertex Form 1. Substitute in the h & k 2. Substitute in the x & y 3. Solve for a 4. Rewrite the equation using the values of h, k &a

Intercept Form When given the intercepts and a point on the graph put the equation in intercept form. 1. Substitute in the p & q values from the intercepts. 2. Substitute in the x & y values from the point. 3. Solve for a 4. Rewrite the equation using the values of p, q & a p q x y

Assignment • p 312 3 -9, 17 -23, 26, 27

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