Quadratic Functions & Models

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Presentation transcript:

Quadratic Functions & Models Chapter 4.10 Quadratic Functions & Models p312 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. 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

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

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

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

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

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

Assignment p312 3-9, 17-23, 26, 27