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Created with Fabric.js 1.4.5 Writing A Quadratic Equation y=ax^2+bx+c Forms Of TheQuadratic Equation Going From standard to vertex form Vertex: y=a(x-h)^2+k Standard:y=ax^2+bx+c From A Table Parts Of The Parabola QUADRATICS -First make sure the X-valuesof the table are going up by one.-Then, y=ax^2+bx+c a= 1/2 of the 2nd change in the y value. To find b value plug a value for x and y in to the equation as well as the a and c values then solve for b. c= y when x=0 y=ax^2+bx+c y=a(x-h)^2+k a is the co-efficient of x^2. A changes the widthand direction of the parabola, it cannot be 0. b changes the value of the vertex. Axis of symmetry is the x value of the vertex. Direction of the opening,whether the parabolais opening up or down. vertex is the highest or lowest point of the parabola. Depending on the a value of the equation the vertex can either be the maximum point or the minimum point of the parabola. h=opposite of x value of vertex k=y value of vertex To find x value of the vertex use equation:x=-b/2a, to find y value plug this into the quadrtic equation. a=a Quad. Equation From A Graph: Parts Of the Quad. Equation c=y intercepta=plug k and h into vertex equation, then plug a x,y value into equation and solve for ab=plug x value of vertex and the a value into x=-b/2a and solve for b. What do a, b, and c do? c changes the y-intercept. Factored:y=a(x+n)(x+m) Real Life Example Bertha's house is being attacked by zombies. She launches a grenade from a catapult at her front door to kill the zombies in her yard. The equation for the grenade's path is: y=-x^2+2x, where Y is the height of the grenade in meters and X is the distance from her front door in meters. If the grenade will explode on impact, how far awaydo the zombies have to be for herto have a direct hit? The answer is 2 meters! This is because: x=(-2+sqrt4)/-2 and (-2-sqrt4)/-2, or x=0, 2 Vocab! Axis of symmetry- X value of vertexMax/Min point- VertexVertex- Min/Max pointQuad. formula- (-b +/- SQRT(b^2 - 4ac))/2aStandard form- y=ax^2+bx+cVertex form- y=a(x-k)^2+h Y X This awesome Info-graphic has been brought to you by Meg Peacher & Isabel Kendall April 8th 2013 D Block
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